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Статті в журналах з теми "Conditions au bord de type Navier"

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Автор: Grafiati

Опубліковано: 28 січня 2024

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1

Siddique, MH, Abdus Samad, and Afzal Husain. "Combined effects of viscosity and surface roughness on electric submersible pump performance." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 231, no. 4 (April 3, 2017): 303–16. http://dx.doi.org/10.1177/0957650917702262.

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An electric submersible pump that lifts crude oil from well bore is a type of multi-stage centrifugal pump. The unexpected wellbore conditions like change in pumping fluid viscosity and sand production severely affect pump performance and eventually lead to breakdown. The present study proposes a numerical approach to understand the effects of fluid viscosity and surface roughness of the flow passages in an electric submersible pump at design and off-design conditions. A three-dimensional numerical analysis was carried out by solving Reynolds-averaged Navier–Stokes equations with shear stress transport turbulence model to characterize performance of the pump. The pumping fluids, i.e., water and crude oils of different viscosities were analyzed for different surface roughness ( Ks) values. The model predictions were compared with a theoretical one-dimensional model for the effect of viscosity and surface roughness. It was found that the disc-friction and the skin-friction losses are sensitive hydraulic losses of which the disc-friction loss increases with increase in viscosity, whereas skin-friction loss decreases with increase in surface roughness at high viscosity. The combined effect of viscosity and roughness showed a complicated behavior and eventually an improvement in pump performance at a higher surface roughness compared to a smoother and lowers surface roughness.

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2

Huijnen, V., L. M. T. Somers, R. S. G. Baert, L. P. H. de Goey, C. Olbricht, A. Sadiki, and J. Janicka. "Study of Turbulent Flow Structures of a Practical Steady Engine Head Flow Using Large-Eddy Simulations." Journal of Fluids Engineering 128, no. 6 (April 21, 2006): 1181–91. http://dx.doi.org/10.1115/1.2353259.

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The prediction performance of two computational fluid dynamics codes is compared to each other and to experimental data of a complex swirling and tumbling flow in a practical complex configuration. This configuration consists of a flow in a production-type heavy-duty diesel engine head with 130-mm cylinder bore. One unsteady Reynolds-averaged Navier-Stokes (URANS)-based simulation and two large-eddy simulations (LES) with different inflow conditions have been performed with the KIVA-3V code. Two LES with different resolutions have been performed with the FASTEST-3D code. The parallelization of the this code allows for a more resolved mesh compared to the KIVA-3V code. This kind of simulations gives a complete image of the phenomena that occur in such configurations, and therefore represents a valuable contribution to experimental data. The complex flow structures gives rise to an inhomogeneous turbulence distribution. Such inhomogeneous behavior of the turbulence is well captured by the LES, but naturally damped by the URANS simulation. In the LES, it is confirmed that the inflow conditions play a decisive role for all main flow features. When no particular treatment of the flow through the runners can be made, the best results are achieved by computing a large part of the upstream region, once performed with the FASTEST-3D code. If the inflow conditions are tuned, all main complex flow structures are also recovered by KIVA-3V. The application of upwinding schemes in both codes is in this respect not crucial.

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3

Amrouche, Cherif, and Nour El Houda Seloula. "On the Stokes equations with the Navier-type boundary conditions." Differential Equations & Applications, no. 4 (2011): 581–607. http://dx.doi.org/10.7153/dea-03-36.

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4

Hu, Weiwei, Yanzhen Wang, Jiahong Wu, Bei Xiao, and Jia Yuan. "Partially dissipative 2D Boussinesq equations with Navier type boundary conditions." Physica D: Nonlinear Phenomena 376-377 (August 2018): 39–48. http://dx.doi.org/10.1016/j.physd.2017.07.003.

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5

Ma, Lina, Rui Chen, Xiaofeng Yang, and Hui Zhang. "Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines." Communications in Computational Physics 21, no. 3 (February 7, 2017): 867–89. http://dx.doi.org/10.4208/cicp.oa-2016-0008.

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AbstractIn this paper, we present some efficient numerical schemes to solve a two-phase hydrodynamics coupled phase field model with moving contact line boundary conditions. The model is a nonlinear coupling system, which consists the Navier-Stokes equations with the general Navier Boundary conditions or degenerated Navier Boundary conditions, and the Allen-Cahn type phase field equations with dynamical contact line boundary condition or static contact line boundary condition. The proposed schemes are linear and unconditionally energy stable, where the energy stabilities are proved rigorously. Various numerical tests are performed to show the accuracy and efficiency thereafter.

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6

Liu, An, Yuan Li, and Rong An. "Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions." Advances in Applied Mathematics and Mechanics 8, no. 6 (September 19, 2016): 932–52. http://dx.doi.org/10.4208/aamm.2014.m595.

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AbstractIn this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the H1 norm and the pressure in the L2 norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.

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7

Li, Yuan, and Rong An. "Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions." Abstract and Applied Analysis 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/125139.

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This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh sizeHin combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh sizeh. The error estimate obtained in this paper shows that ifH,h, andεcan be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

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8

Kučera, Petr, and Jiří Neustupa. "OnL3-stability of strong solutions of the Navier–Stokes equations with the Navier-type boundary conditions." Journal of Mathematical Analysis and Applications 405, no. 2 (September 2013): 731–37. http://dx.doi.org/10.1016/j.jmaa.2013.04.037.

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9

Pineau, Benjamin, and Xinwei Yu. "On Prodi–Serrin type conditions for the 3D Navier–Stokes equations." Nonlinear Analysis 190 (January 2020): 111612. http://dx.doi.org/10.1016/j.na.2019.111612.

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10

Guo, Zhengguang, Petr Kučera, and Zdenek Skalak. "Navier–Stokes equations: regularity criteria in terms of the derivatives of several fundamental quantities along the streamlines—the case of a bounded domain." Nonlinearity 35, no. 11 (October 13, 2022): 5880–902. http://dx.doi.org/10.1088/1361-6544/ac8e4c.

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Abstract In this paper we deal with the conditional regularity of the weak solutions of the Navier–Stokes equations on a bounded domain endowed with Navier boundary conditions, Navier-type boundary conditions or Dirichlet boundary conditions. We prove the regularity criteria which are based on the directional derivatives of several fundamental quantities along the streamlines, namely the velocity magnitude, the kinetic energy, the pressure, the velocity field and the Bernoulli pressure. In striking contrast to the known criteria in which the mentioned quantities were differentiated along a fixed vector, our criteria are mostly optimal for the whole range of parameters and have a clear physical meaning.

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11

Saidi, Fouad. "ON THE NAVIER-STOKES EQUATION WITH SLIP BOUNDARY CONDITIONS OF FRICTION TYPE." Mathematical Modelling and Analysis 12, no. 3 (September 30, 2007): 389–98. http://dx.doi.org/10.3846/1392-6292.2007.12.389-398.

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In this paper we deal with the boundary value problem for the stationary flow for Newtonian and incompressible fluid governed by the Navier‐Stokes equation with slip boundary conditions of friction type, mostly by means of variational inequalities. Among others, theorems concerning existence and uniqueness of weak solutions are presented.

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12

Wang, Teng, and Yi Wang. "Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions." Communications on Pure & Applied Analysis 20, no. 7-8 (2021): 2811. http://dx.doi.org/10.3934/cpaa.2021080.

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<p style="text-indent:20px;">We are concerned with the large-time asymptotic behaviors towards the planar rarefaction wave to the three-dimensional (3D) compressible and isentropic Navier-Stokes equations in half space with Navier boundary conditions. It is proved that the planar rarefaction wave is time-asymptotically stable for the 3D initial-boundary value problem of the compressible Navier-Stokes equations in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^+\times \mathbb{T}^2 $\end{document}</tex-math></inline-formula> with arbitrarily large wave strength. Compared with the previous work [<xref ref-type="bibr" rid="b17">17</xref>, <xref ref-type="bibr" rid="b16">16</xref>] for the whole space problem, Navier boundary conditions, which state that the impermeable wall condition holds for the normal velocity and the fluid tangential velocity is proportional to the tangential component of the viscous stress tensor on the boundary, are crucially used for the stability analysis of the 3D initial-boundary value problem.</p>

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13

Cruzeiro, Ana Bela, and Iván Torrecilla. "On a 2D stochastic Euler equation of transport type: Existence and geometric formulation." Stochastics and Dynamics 15, no. 01 (December 7, 2014): 1450012. http://dx.doi.org/10.1142/s0219493714500129.

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We prove weak existence of Euler equation (or Navier–Stokes equation) perturbed by a multiplicative noise on bounded domains of ℝ2 with Dirichlet boundary conditions and with periodic boundary conditions. Solutions are H1 regular. The equations are of transport type.

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14

Duarte-Leiva, Cristian, Sebastián Lorca, and Exequiel Mallea-Zepeda. "A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions." Symmetry 13, no. 8 (July 26, 2021): 1348. http://dx.doi.org/10.3390/sym13081348.

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Micropolar fluids are fluids with microstructure and belong to a class of fluids with asymmetric stress tensor that called Polar fluids, and include, as a special case, the well-established Navier–Stokes model. In this work we study a 3D micropolar fluids model with Navier boundary conditions without friction for the velocity field and homogeneous Dirichlet boundary conditions for the angular velocity. Using the Galerkin method, we prove the existence of weak solutions and establish a Prodi–Serrin regularity type result which allow us to obtain global-in-time strong solutions at finite time.

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15

sci, Weifeng Zhang &. Shuo Zhang. "Order Reduced Methods for Quad-Curl Equations with Navier Type Boundary Conditions." Journal of Computational Mathematics 38, no. 4 (June 2020): 565–79. http://dx.doi.org/10.4208/jcm.1901-m2018-0150.

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16

da Veiga, H. Beirão, and Francesca Crispo. "Sharp Inviscid Limit Results under Navier Type Boundary Conditions. An Lp Theory." Journal of Mathematical Fluid Mechanics 12, no. 3 (April 20, 2009): 397–411. http://dx.doi.org/10.1007/s00021-009-0295-4.

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17

Monniaux, Sylvie, and El Maati Ouhabaz. "The Incompressible Navier–Stokes System with Time-Dependent Robin-Type Boundary Conditions." Journal of Mathematical Fluid Mechanics 17, no. 4 (October 1, 2015): 707–22. http://dx.doi.org/10.1007/s00021-015-0227-4.

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18

Rezapour, Shahram, Brahim Tellab, Chernet Tuge Deressa, Sina Etemad, and Kamsing Nonlaopon. "H-U-Type Stability and Numerical Solutions for a Nonlinear Model of the Coupled Systems of Navier BVPs via the Generalized Differential Transform Method." Fractal and Fractional 5, no. 4 (October 13, 2021): 166. http://dx.doi.org/10.3390/fractalfract5040166.

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This paper is devoted to generalizing the standard system of Navier boundary value problems to a fractional system of coupled sequential Navier boundary value problems by using terms of the Caputo derivatives. In other words, for the first time, we design a multi-term fractional coupled system of Navier equations under the fractional boundary conditions. The existence theory is studied regarding solutions of the given coupled sequential Navier boundary problems via the Krasnoselskii’s fixed-point theorem on two nonlinear operators. Moreover, the Banach contraction principle is applied to investigate the uniqueness of solution. We then focus on the Hyers–Ulam-type stability of its solution. Furthermore, the approximate solutions of the proposed coupled fractional sequential Navier system are obtained via the generalized differential transform method. Lastly, the results of this research are supported by giving simulated examples.

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19

Lebrimchi, Hafid, Mohamed Talbi, Mohammed Massar, and Najib Tsouli. "On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions." Abstract and Applied Analysis 2021 (November 29, 2021): 1–8. http://dx.doi.org/10.1155/2021/4514044.

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In this article, we study the existence of solutions for nonlocal p x -biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.

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20

Sorokina, E. M., and A. G. Obukhov. "NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING." Oil and Gas Studies, no. 3 (June 30, 2015): 87–93. http://dx.doi.org/10.31660/0445-0108-2015-3-87-93.

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To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

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21

Doumate, Jonas Tele, Lawoue Robert Toyou, and Liamidi A. Leadi. "On eigenvalues of p-biharmonic operator and associated concave-convex type equation." Gulf Journal of Mathematics 13, no. 1 (July 19, 2022): 54–87. http://dx.doi.org/10.56947/gjom.v13i1.927.

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In this article, we are interested in the simplicity and the existence of the first eigensurface for the third order spectrum of p-biharmonic operator plus potential with weights and the existence of multiple solutions for associated concave-convex type equation under Navier boundary conditions.

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22

Bathory, Michal, and Ulisse Stefanelli. "Variational resolution of outflow boundary conditions for incompressible Navier–Stokes." Nonlinearity 35, no. 11 (September 29, 2022): 5553–92. http://dx.doi.org/10.1088/1361-6544/ac8fd8.

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Abstract This paper focuses on the so-called weighted inertia-dissipation-energy variational approach for the approximation of unsteady Leray–Hopf solutions of the incompressible Navier–Stokes system. Initiated in (Ortiz et al 2018 Nonlinearity 31 5664–82), this variational method is here extended to the case of non-Newtonian fluids with power-law index r ⩾ 11/5 in three space dimension and large nonhomogeneous data. Moreover, boundary conditions are not imposed on some parts of boundaries, representing, e.g., outflows. Correspondingly, natural boundary conditions arise from the minimisation. In particular, at walls we recover boundary conditions of Navier-slip type. At outflows and inflows, we obtain the condition − 1 2 | v | 2 n + T n = 0 . This provides the first theoretical explanation for the onset of such boundary conditions.

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23

Seregin, G., and W. Wang. "Sufficient conditions on Liouville type theorems for the 3D steady Navier–Stokes equations." St. Petersburg Mathematical Journal 31, no. 2 (February 4, 2020): 387–93. http://dx.doi.org/10.1090/spmj/1603.

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24

Zhang, Qi, and Qing Miao. "Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator." Journal of Mathematics 2021 (July 24, 2021): 1–12. http://dx.doi.org/10.1155/2021/5547669.

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Анотація:

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

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25

Boldrini, José Luiz, and João Paulo Lukaszczyk. "Incompressible flow in granulated porous media with null initial velocity." Ciência e Natura 20, no. 20 (December 14, 1998): 07. http://dx.doi.org/10.5902/2179460x26813.

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In this work we study a Navier-Stokes type equation which models the flow of a viscous, homogeneous and incompressible fluid in a isotropic granular (non consolidated) porous media. Using point fixed type arguments we obtain conditions for existence of solution for the equation in Hölder's spaces.

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26

Neustupa, Jiří, and Hind Al Baba. "The interior regularity of pressure associated with a weak solution to the Navier–Stokes equations with the Navier-type boundary conditions." Journal of Mathematical Analysis and Applications 463, no. 1 (July 2018): 222–34. http://dx.doi.org/10.1016/j.jmaa.2018.03.017.

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27

Zhang, Qi, and Qing Miao. "Existence and Multiplicity of Solutions for a Biharmonic Equation with p(x)-Kirchhoff Type." Discrete Dynamics in Nature and Society 2021 (December 2, 2021): 1–8. http://dx.doi.org/10.1155/2021/8454755.

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Based on the basic theory and critical point theory of variable exponential Lebesgue Sobolev space, this paper investigates the existence and multiplicity of solutions for a class of nonlocal elliptic equations with Navier boundary value conditions when (AR) condition does not hold and improves or generalizes the original conclusions.

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28

Ciuperca, I. S., E. Feireisl, M. Jai, and A. Petrov. "A rigorous derivation of the stationary compressible Reynolds equation via the Navier–Stokes equations." Mathematical Models and Methods in Applied Sciences 28, no. 04 (April 2018): 697–732. http://dx.doi.org/10.1142/s0218202518500185.

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Анотація:

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier–Stokes system on a thin domain. In particular, the existence of solutions to the Navier–Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the one-dimensional case.

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29

Zhuo, Ran, Fengquan Li, and Boqiang Lv. "Liouville type theorems for Schrödinger system with Navier boundary conditions in a half space." Communications on Pure & Applied Analysis 13, no. 3 (2014): 977–90. http://dx.doi.org/10.3934/cpaa.2014.13.977.

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30

Filo, Ján, and Anna Zaušková. "2D Navier–Stokes Equations in a Time Dependent Domain with Neumann Type Boundary Conditions." Journal of Mathematical Fluid Mechanics 12, no. 1 (June 10, 2008): 1–46. http://dx.doi.org/10.1007/s00021-008-0274-1.

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31

Wu, Yong, Said Taarabti, Zakaria El Allali, Khalil Ben Hadddouch, and Jiabin Zuo. "A Class of Fourth-Order Symmetrical Kirchhoff Type Systems." Symmetry 14, no. 8 (August 8, 2022): 1630. http://dx.doi.org/10.3390/sym14081630.

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Анотація:

This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(·)&q(·)-Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri’s critical point theorem, we can find a proper conditions to ensure that the perturbed fourth-order of (p(x),q(x))-Kirchhoff systems has at least three weak solutions. We have extended and improved some recent results. The complexity of the combination of variable exponent theory and fourth-order Kirchhoff systems makes the results of this work novel and new contribution. Finally, a very concrete example is given to illustrate the applications of our results.

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32

Amrouche, Chérif, and Imane Boussetouan. "Vector Potentials with Mixed Boundary Conditions. Application to the Stokes Problem with Pressure and Navier-type Boundary Conditions." SIAM Journal on Mathematical Analysis 53, no. 2 (January 2021): 1745–84. http://dx.doi.org/10.1137/20m1332189.

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33

Benkirane, Abdelmoujib, Mostafa El Moumni, and Aziz Fri. "An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application." Chinese Journal of Mathematics 2014 (April 29, 2014): 1–7. http://dx.doi.org/10.1155/2014/549051.

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Анотація:

The aim of this paper is to extend the usual framework of PDE with Au=-div ax,u,∇u to include a large class of cases with Au=∑β≤α-1βDβAβx,u,∇u,…,∇αu, whose coefficient Aβ satisfies conditions (including growth conditions) which guarantee the solvability of the problem Au=f. This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation.

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34

Angermann, L. "Transport-stabilized Semidiscretizations of the Incompressible Navier—Stokes Equations." Computational Methods in Applied Mathematics 6, no. 3 (2006): 239–63. http://dx.doi.org/10.2478/cmam-2006-0013.

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AbstractWithin the framework of finite element methods, the paper investigates a general approximation technique for the nonlinear convective term of Navier — Stokes equations. The approach is based on an upwind method of the finite volume type. It has been proved that the discrete convective term satisfies the well-known collection of sufficient conditions for convergence of the finite element solution. For a particular nonconforming scheme, the assumptions have been verified in detail and the estimate of the semidiscrete velocity error has been proved.

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35

Barbu, Viorel, Giuseppe Da Prato, and Luciano Tubaro. "A Reflection Type Problem for the Stochastic 2-D Navier-Stokes Equations with Periodic Conditions." Electronic Communications in Probability 16 (2011): 304–13. http://dx.doi.org/10.1214/ecp.v16-1633.

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36

Sukhinov, A. I., V. V. Sidoryakina, and S. V. Protsenko. "Coastal wave processes numerical modeling for large valley-type reservoirs." Journal of Physics: Conference Series 2131, no. 3 (December 1, 2021): 032051. http://dx.doi.org/10.1088/1742-6596/2131/3/032051.

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Анотація:

Abstract The problem of modeling sediment transport and wave processes of large valley-type reservoir under non-stationary conditions of the hydrological cycle active phase (spring-autumn period) is considered. Coupled 2D sediment transport model and 3D wave hydrodynamics was considered to describe these processes, which uses the Navier-Stokes equations. The wave hydrodynamics model is applied to large reservoir of the valley type, such as Tsimlyansky reservoir. Detailed numerical experiments were performed taking into account the real coastline geometry and the bottom relief of the Tsimlyansk reservoir southwestern part. The developed complex of models and programs allows to predict reshaping the bottom relief and coastline under various hydrometeorological conditions. The results of modeling can be in demand when planning water management activities in valley-type reservoirs.

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37

Farazmand, M. "An adjoint-based approach for finding invariant solutions of Navier–Stokes equations." Journal of Fluid Mechanics 795 (April 14, 2016): 278–312. http://dx.doi.org/10.1017/jfm.2016.203.

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We consider the incompressible Navier–Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and travelling-wave solutions of the Navier–Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of $100\,\%$ is observed, leading to the discovery of $21$ new steady-state and travelling-wave solutions at Reynolds number $Re=40$. Some of the new invariant solutions have spatially localized structures that were previously believed to exist only on domains with large aspect ratios. We show that one of the newly found steady-state solutions underpins the temporal intermittencies, i.e. high energy dissipation episodes of the flow. More precisely, it is shown that each intermittent episode of a generic turbulent trajectory corresponds to its close passage to this equilibrium solution.

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38

Kondrashuk, Igor, Eduardo Alfonso Notte-Cuello, Mariano Poblete-Cantellano, and Marko Antonio Rojas-Medar. "Periodic Solution and Asymptotic Stability for the Magnetohydrodynamic Equations with Inhomogeneous Boundary Condition." Axioms 8, no. 2 (April 11, 2019): 44. http://dx.doi.org/10.3390/axioms8020044.

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We show, using the spectral Galerkin method together with compactness arguments, the existence and uniqueness of the periodic strong solutions for the magnetohydrodynamic-type equations with inhomogeneous boundary conditions. Furthermore, we study the asymptotic stability for the time periodic solution for this system. In particular, when the magnetic field h ( x , t ) is zero, we obtain the existence, uniqueness, and asymptotic behavior of the strong solutions to the Navier–Stokes equations with inhomogeneous boundary conditions.

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39

Qian, Chenyin. "The regularity criterion for the 3D Navier–Stokes equations involving end-point Prodi–Serrin type conditions." Applied Mathematics Letters 75 (January 2018): 37–42. http://dx.doi.org/10.1016/j.aml.2017.06.014.

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40

Al Baba, Hind, Chérif Amrouche, and Miguel Escobedo. "Semi-Group Theory for the Stokes Operator with Navier-Type Boundary Conditions on L p -Spaces." Archive for Rational Mechanics and Analysis 223, no. 2 (November 14, 2016): 881–940. http://dx.doi.org/10.1007/s00205-016-1048-1.

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41

Parhi, Dayal R., and A. K. Behera. "VIBRATION ANALYSIS OF CANTILEVER TYPE CRACKED ROTOR IN VISCOUS FLUID." Transactions of the Canadian Society for Mechanical Engineering 27, no. 3 (June 2003): 147–73. http://dx.doi.org/10.1139/tcsme-2003-0008.

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The increasing utilisation of rotors in industries and other fields require interpretation of their vibration characteristics and failure conditions. Therefore, computer programmes that have been used will have to be constantly updated. This paper deals with the cantilever type rotor containing a transverse crack subjected to viscous medium. Damping effect and virtual mass effect are taken into account through Navier Stokes equation. The stiff-ness of the cracked shaft is evaluated from the theory of fracture mechanics. For analysis rotor with different crack depth, subjected different viscous medium is considered. The numerical result obtained from theoretical analysis is compared with the experimental results, which agree well.

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42

Kračmar, S., and J. Neustupa. "A weak solvability of a steady variational inequality of the Navier–Stokes type with mixed boundary conditions." Nonlinear Analysis: Theory, Methods & Applications 47, no. 6 (August 2001): 4169–80. http://dx.doi.org/10.1016/s0362-546x(01)00534-x.

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43

Rahal, Belgacem. "Existence results of infinitely many solutions for p(x)-Kirchhoff type triharmonic operator with Navier boundary conditions." Journal of Mathematical Analysis and Applications 478, no. 2 (October 2019): 1133–46. http://dx.doi.org/10.1016/j.jmaa.2019.06.006.

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44

GIUNTA, G., F. BISCANI, S. BELOUETTAR, and E. CARRERA. "ANALYSIS OF THIN-WALLED BEAMS VIA A ONE-DIMENSIONAL UNIFIED FORMULATION THROUGH A NAVIER-TYPE SOLUTION." International Journal of Applied Mechanics 03, no. 03 (September 2011): 407–34. http://dx.doi.org/10.1142/s1758825111001056.

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A unifying approach to formulate several axiomatic theories for beam structures is addressed in this paper. A N-order polynomials approximation is assumed on the beam cross-section for the displacement unknown variables, N being a free parameter of the formulation. Classical beam theories, such as Euler–Bernoulli's and Timoshenko's, are obtained as particular cases. According to the proposed unified formulation, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The linear static analysis of thin-walled beams is carried out through a closed form, Navier-type solution. Simply supported beams are, therefore, presented. Box, C- and I-shaped cross-sections are accounted for. Slender and deep beams are investigated. Bending and torsional loadings are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and the loading conditions.

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45

Takahashi, Koichi. "Three-Dimensional Unsteady Axisymmetric Viscous Beltrami Vortex Solutions to the Navier–Stokes Equations." J 6, no. 3 (August 5, 2023): 460–76. http://dx.doi.org/10.3390/j6030030.

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This paper is aimed at eliciting consistency conditions for the existence of unsteady incompressible axisymmetric swirling viscous Beltrami vortices and explicitly constructing solutions that obey the conditions as well as the Navier–Stokes equations. By Beltrami flow, it is meant that vorticity, i.e., the curl of velocity, is proportional to velocity at any local point in space and time. The consistency conditions are derived for the proportionality coefficient, the velocity field and external force. The coefficient, whose dimension is of [length−1], is either constant or nonconstant. In the former case, the well-known exact nondivergent three-dimensional unsteady vortex solutions are obtained by solving the evolution equations for the stream function directly. In the latter case, the consistency conditions are given by nonlinear equations of the stream function, one of which corresponds to the Bragg–Hawthorne equation for steady inviscid flow. Solutions of a novel type are found by numerically solving the nonlinear constraint equation at a fixed time. Time dependence is recovered by taking advantage of the linearity of the evolution equation of the stream function. The proportionality coefficient is found to depend on space and time. A phenomenon of partial restoration of the broken scaling invariance is observed at short distances.

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46

Allgeyer, Sebastien, Marie-Odile Bristeau, David Froger, Raouf Hamouda, V. Jauzein, Anne Mangeney, Jacques Sainte-Marie, Fabien Souillé, and Martin Vallée. "Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 6 (November 2019): 1981–2024. http://dx.doi.org/10.1051/m2an/2019044.

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In this paper we propose a stable and robust strategy to approximate the 3D incompressible hydrostatic Euler and Navier–Stokes systems with free surface. Compared to shallow water approximation of the Navier–Stokes system, the idea is to use a Galerkin type approximation of the velocity field with piecewise constant basis functions in order to obtain an accurate description of the vertical profile of the horizontal velocity. Such a strategy has several advantages. It allows to rewrite the Navier–Stokes equations under the form of a system of conservation laws with source terms,the easy handling of the free surface, which does not require moving meshes,the possibility to take advantage of robust and accurate numerical techniques developed in extensive amount for Shallow Water type systems. Compared to previous works of some of the authors, the three dimensional case is studied in this paper. We show that the model admits a kinetic interpretation including the vertical exchanges terms, and we use this result to formulate a robust finite volume scheme for its numerical approximation. All the aspects of the discrete scheme (fluxes, boundary conditions, ...) are completely described and the stability properties of the proposed numerical scheme (well-balancing, positivity of the water depth, ...) are discussed. We validate the model and the discrete scheme with some numerical academic examples (3D non stationary analytical solutions) and illustrate the capability of the discrete model to reproduce realistic tsunami waves propagation, tsunami runup and complex 3D hydrodynamics in a raceway.

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47

Haslinger, Jaroslav, Radek Kučera, Václav Šátek, and Taoufik Sassi. "Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation." Mathematics and Mechanics of Solids 23, no. 3 (October 11, 2017): 294–307. http://dx.doi.org/10.1177/1081286517716222.

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The paper analyzes the Stokes system with threshold slip boundary conditions of Navier type. Based on the fixed-point formulation we prove the existence of a solution for a class of solution-dependent slip functions g satisfying an appropriate growth condition and its uniqueness provided that g is one-sided Lipschitz continuous. Further we study under which conditions the respective fixed-point mapping is contractive. To discretize the problem we use P1-bubble/P1 elements. Properties of discrete models in dependence on the discretization parameter are analysed and convergence results are established. In the second part of the paper we briefly describe the duality approach used in computations and present results of a model example.

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48

Turan, Muhittin, and Volkan Kahya. "Use of trigonometric series functions in free vibration analysis of laminated composite beams." Challenge Journal of Structural Mechanics 6, no. 2 (June 17, 2020): 61. http://dx.doi.org/10.20528/cjsmec.2020.02.002.

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In this study, free vibration analysis of layered composite beams is performed by using an analytical method based on trigonometric series. Based on the first-order shear deformation beam theory, the governing equations are derived from the Lagrange’s equations. Appropriate trigonometric series functions are selected to satisfy the end conditions of the beam. Navier-type solution is used to obtain natural frequencies. Natural frequencies are calculated for different end conditions and lamina stacking. It was seen that the slenderness, E11/E22 and fiber angle have a significant effect on natural frequency. The results of the study are quite compatible with the literature.

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49

Coronel, Aníbal, Fernando Huancas, Alex Tello, and Marko Rojas-Medar. "New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations." Axioms 10, no. 3 (August 29, 2021): 205. http://dx.doi.org/10.3390/axioms10030205.

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We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.

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50

Clopeau, Thierry, Andro Mikelic, and Raoul Robert. "On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions." Nonlinearity 11, no. 6 (November 1, 1998): 1625–36. http://dx.doi.org/10.1088/0951-7715/11/6/011.

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