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Journal articles on the topic 'Limite incompressible'

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Published: 6 July 2024

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1

Lions, Pierre-Louis, and Nader Masmoudi. "Une approche locale de la limite incompressible." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 329, no. 5 (September 1999): 387–92. http://dx.doi.org/10.1016/s0764-4442(00)88611-5.

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2

Berry, Ray A., and Richard C. Martineau. "ICONE15-10278 EXAMINATION OF THE PCICE METHOD IN THE NEARLY INCOMPRESSIBLE, AS WELL AS STRICTLY INCOMPRESSIBLE, LIMITS." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2007.15 (2007): _ICONE1510. http://dx.doi.org/10.1299/jsmeicone.2007.15._icone1510_137.

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3

Howards, Hugh Nelson. "Limits of incompressible surfaces." Topology and its Applications 99, no. 1 (November 1999): 117–22. http://dx.doi.org/10.1016/s0166-8641(98)00083-2.

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4

Feireisl, Eduard, Šárka Nečasová, and Yongzhong Sun. "Inviscid incompressible limits on expanding domains." Nonlinearity 27, no. 10 (September 5, 2014): 2465–77. http://dx.doi.org/10.1088/0951-7715/27/10/2465.

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5

Miles, Christopher J., and Charles R. Doering. "Diffusion-limited mixing by incompressible flows." Nonlinearity 31, no. 5 (April 16, 2018): 2346–59. http://dx.doi.org/10.1088/1361-6544/aab1c8.

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6

Caggio, Matteo, and Šárka Nečasová. "Inviscid incompressible limits for rotating fluids." Nonlinear Analysis 163 (November 2017): 1–18. http://dx.doi.org/10.1016/j.na.2017.07.002.

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7

Wang, Jiawei. "Incompressible limit of nonisentropic Hookean elastodynamics." Journal of Mathematical Physics 63, no. 6 (June 1, 2022): 061506. http://dx.doi.org/10.1063/5.0080539.

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We study the incompressible limit of the compressible nonisentropic Hookean elastodynamics with general initial data in the whole space [Formula: see text]. First, we obtain the uniform estimates of the solutions in [Formula: see text] for s > d/2 + 1 being even and the existence of classic solutions on a time interval independent of the Mach number. Then, we prove that the solutions converge to the incompressible elastodynamic equations as the Mach number tends to zero.

8

Schochet, Steven. "The incompressible limit in nonlinear elasticity." Communications in Mathematical Physics 102, no. 2 (June 1985): 207–15. http://dx.doi.org/10.1007/bf01229377.

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9

Druet, Pierre-Etienne. "Incompressible limit for a fluid mixture." Nonlinear Analysis: Real World Applications 72 (August 2023): 103859. http://dx.doi.org/10.1016/j.nonrwa.2023.103859.

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10

Sideris, Thomas C., and Becca Thomases. "Global existence for three-dimensional incompressible isotropic elastodynamics via the incompressible limit." Communications on Pure and Applied Mathematics 58, no. 6 (2005): 750–88. http://dx.doi.org/10.1002/cpa.20049.

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11

Feireisl, Eduard, Bum Ja Jin, and Antonín Novotný. "Inviscid incompressible limits of strongly stratified fluids." Asymptotic Analysis 89, no. 3-4 (2014): 307–29. http://dx.doi.org/10.3233/asy-141231.

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12

Wang, Shu. "The Zero-Mach Limit of Compressible Euler Equations." Applied Mechanics and Materials 275-277 (January 2013): 518–21. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.518.

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The aim of this paper is to prove that compressible Euler equations in two and three space dimensions converge to incompressible Euler equations in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the initial velocity, or the time interval. We assume instead that the incompressible flows exists and is reasonably smooth on a given time interval, and prove that compressible flows converge uniformly on that time interval.

13

Gambin, B., and W. Bielski. "Incompressible limit for a magnetostrictive energy functional." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 4 (December 1, 2013): 1025–30. http://dx.doi.org/10.2478/bpasts-2013-0110.

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Abstract The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

14

Shi, Fei. "Incompressible limit of Euler equations with damping." Electronic Research Archive 30, no. 1 (2021): 126–39. http://dx.doi.org/10.3934/era.2022007.

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<abstract><p>The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.</p></abstract>

15

Sivaloganathan, J. "Cavitation, the incompressible limit, and material inhomogeneity." Quarterly of Applied Mathematics 49, no. 3 (January 1, 1991): 521–41. http://dx.doi.org/10.1090/qam/1121684.

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16

Lions, P. L., and N. Masmoudi. "Incompressible limit for a viscous compressible fluid." Journal de Mathématiques Pures et Appliquées 77, no. 6 (June 1998): 585–627. http://dx.doi.org/10.1016/s0021-7824(98)80139-6.

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17

NOR AZWADI, C. S., and T. TANAHASHI. "SIMPLIFIED THERMAL LATTICE BOLTZMANN IN INCOMPRESSIBLE LIMIT." International Journal of Modern Physics B 20, no. 17 (July 10, 2006): 2437–49. http://dx.doi.org/10.1142/s0217979206034789.

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In this paper, an incompressible thermohydrodynamics for the lattice Boltzmann scheme is developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that a new lattice of four-velocity model for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. This model is validated by the numerical simulation of the porous plate couette flow problem where the analytical solution exists and the natural convection flows in a square cavity.

18

Wu, Weijun, Fujun Zhou, and Yongsheng Li. "Incompressible Euler–Poisson limit of the Vlasov–Poisson–Boltzmann system." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 081502. http://dx.doi.org/10.1063/5.0054024.

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This paper is to justify the incompressible Euler–Poisson limit of the Vlasov–Poisson–Boltzmann system in the incompressible hyperbolic regime. The proof is based on a new [Formula: see text] framework, which consists of the [Formula: see text] energy estimate and the weighted [Formula: see text] estimate of the Vlasov–Poisson–Boltzmann system.

19

McMillan, B. F., R. L. Dewar, and R. G. Storer. "A comparison of incompressible limits for resistive plasmas." Plasma Physics and Controlled Fusion 46, no. 7 (May 25, 2004): 1027–38. http://dx.doi.org/10.1088/0741-3335/46/7/003.

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20

Feireisl, Eduard, Ondřej Kreml, Šárka Nečasová, Jiří Neustupa, and Jan Stebel. "Incompressible Limits of Fluids Excited by Moving Boundaries." SIAM Journal on Mathematical Analysis 46, no. 2 (January 2014): 1456–71. http://dx.doi.org/10.1137/130916916.

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21

Liu, Zhengrong, and Hongjun Yu. "The diffusive limit of Boltzmann equation in torus." Nonlinearity 37, no. 7 (May 20, 2024): 075003. http://dx.doi.org/10.1088/1361-6544/ad4502.

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Abstract The Boltzmann equation of kinetic theory gives a statistical description of a gas of interacting particles. It is well known that the Boltzmann equation is related to the Euler and Navier–Stokes equations in the field of gas dynamics. In this paper we are concerned with the incompressible Navier–Stokes–Fourier limit of the Boltzmann equation. We prove the incompressible Navier–Stokes–Fourier limit globally in time and the time decay rate of the solution to the rescaled Boltzmann equation in a torus. For ɛ small, by using the truncated expansion and L x , v 2 – L x , v ∞ method, we prove such a limit for the general potentials γ ∈ ( − 3 , 1 ] .

22

Caggio, Matteo. "Inviscid incompressible limit for compressible micro-polar fluids." Nonlinear Analysis 216 (March 2022): 112695. http://dx.doi.org/10.1016/j.na.2021.112695.

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23

Luo, Yi-Long, and Yangjun Ma. "Zero inertia limit of incompressible Qian–Sheng model." Analysis and Applications 20, no. 02 (November 9, 2021): 221–84. http://dx.doi.org/10.1142/s0219530521500184.

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The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.

24

Secchi, Paolo. "On the incompressible limit of inviscid compressible fluids." ANNALI DELL UNIVERSITA DI FERRARA 46, no. 1 (December 2000): 21–33. http://dx.doi.org/10.1007/bf02837288.

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25

Danchin, Raphaël. "The inviscid limit for density-dependent incompressible fluids." Annales de la faculté des sciences de Toulouse Mathématiques 15, no. 4 (2006): 637–88. http://dx.doi.org/10.5802/afst.1133.

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26

Jiang, Song, Qiangchang Ju, and Fucai Li. "Incompressible Limit of the Nonisentropic Ideal Magnetohydrodynamic Equations." SIAM Journal on Mathematical Analysis 48, no. 1 (January 2016): 302–19. http://dx.doi.org/10.1137/15m102842x.

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27

Mazzucato, A. L. "On the zero viscosity limit in incompressible fluids." Physica Scripta T132 (December 2008): 014002. http://dx.doi.org/10.1088/0031-8949/2008/t132/014002.

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28

Jagodziński, S., and M. Lachowicz. "Incompressible Navier-Stokes limit for the Enskog equation." Applied Mathematics Letters 13, no. 7 (October 2000): 107–11. http://dx.doi.org/10.1016/s0893-9659(00)00084-7.

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29

高, 婷婷. "Incompressible Limit of the Two Dimensional Boltzmann Equation." Pure Mathematics 10, no. 02 (2020): 128–38. http://dx.doi.org/10.12677/pm.2020.102019.

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30

HAO, Yihang, and Xiangao LIU. "Incompressible limit of a compressible liquid crystals system." Acta Mathematica Scientia 33, no. 3 (May 2013): 781–96. http://dx.doi.org/10.1016/s0252-9602(13)60038-7.

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31

Breit, Dominic, Eduard Feireisl, and Martina Hofmanová. "Incompressible Limit for Compressible Fluids with Stochastic Forcing." Archive for Rational Mechanics and Analysis 222, no. 2 (May 27, 2016): 895–926. http://dx.doi.org/10.1007/s00205-016-1014-y.

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32

Ju, Qiangchang, and Jianjun Xu. "Zero-Mach limit of the compressible Navier–Stokes–Korteweg equations." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 111503. http://dx.doi.org/10.1063/5.0124119.

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We consider the Cauchy problem for the compressible Navier–Stokes–Korteweg system in three dimensions. Under the assumption of the global existence of strong solutions to incompressible Navier–Stokes equations, we demonstrate that the compressible Navier–Stokes–Korteweg system admits a global unique strong solution without smallness restrictions on initial data when the Mach number is sufficiently small. Furthermore, we derive the uniform convergence of strong solutions for compressible Navier–Stokes–Korteweg equations toward those for incompressible Navier–Stokes equations as long as the solution of the limiting system exists.

33

Sahay, Pratap N., and Tobias M. Müller. "Diffusion in deformable porous media: Incompressible flow limit and implications for permeability estimation from microseismicity." GEOPHYSICS 85, no. 2 (February 24, 2020): A13—A17. http://dx.doi.org/10.1190/geo2019-0510.1.

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Injecting fluid in a borehole often has been observed to be causally related with seismicity. The standard explanation assumes that a stress perturbation spreads out and triggers rock failure. It has been suggested that this spreading is governed by Biot’s slow P-wave, which is a diffusion process associated with compressible fluid flow. Because the diffusion constant is proportional to the permeability, the space-time evolution of seismicity is exploited to estimate the permeability. However, the more plausible scenario of incompressible fluid flow is beyond the scope of Biot’s theory. We have examined the diffusion process predicted by the de la Cruz-Spanos poroelasticity theory when the flow is incompressible. Then, the diffusion constant can be two orders of magnitude larger than the Biot diffusion constant. We have determined that seismicity-based permeability estimates strongly depend on whether the flow is compressible or incompressible. Ignoring the incompressible flow scenario might lead to an overestimation of the permeability.

34

BERRY, Ray A., and Richard C. MARTINEAU. "Examination of the PCICE Method in the Nearly Incompressible, as well as Strictly Incompressible, Limits." Journal of Power and Energy Systems 2, no. 2 (2008): 598–610. http://dx.doi.org/10.1299/jpes.2.598.

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35

Hmidi, Taoufik, and Samira Sulaiman. "Incompressible limit for the two-dimensional isentropic Euler system with critical initial data." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 6 (December 2014): 1127–54. http://dx.doi.org/10.1017/s0308210512000509.

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We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

36

Gouin, Henri, and Tommaso Ruggeri. "A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials." International Journal of Non-Linear Mechanics 47, no. 6 (July 2012): 688–93. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.11.005.

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37

Banda, M. K., M. Seaı̈d, A. Klar, and L. Pareschi. "Compressible and incompressible limits for hyperbolic systems with relaxation." Journal of Computational and Applied Mathematics 168, no. 1-2 (July 2004): 41–52. http://dx.doi.org/10.1016/j.cam.2003.05.013.

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38

Kwon, Young-Sam, and Konstantina Trivisa. "On the incompressible limits for the full magnetohydrodynamics flows." Journal of Differential Equations 251, no. 7 (October 2011): 1990–2023. http://dx.doi.org/10.1016/j.jde.2011.04.016.

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39

Gu, Xiaoyu, Yaobin Ou, and Lu Yang. "Incompressible limit of isentropic magnetohydrodynamic equations with ill-prepared data in bounded domains." Journal of Mathematical Physics 64, no. 3 (March 1, 2023): 031501. http://dx.doi.org/10.1063/5.0140349.

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This paper rigorously justifies the incompressible limit of strong solutions to isentropic compressible magnetohydrodynamic equations with ill-prepared initial data in a three-dimensional bounded domain as the Mach number goes to zero. In both cases of viscous and inviscid magnetic fields, we establish a new energy functional with weight to obtain uniform estimates for strong solutions with respect to the Mach number. Then, we prove the weak convergence of a velocity and the strong convergence of a magnetic field and the divergence-free component of a velocity field, which yields the corresponding incompressible limit.

40

Rachid, Mohamad. "Incompressible Navier-Stokes-Fourier limit from the Landau equation." Kinetic & Related Models 14, no. 4 (2021): 599. http://dx.doi.org/10.3934/krm.2021017.

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<p style='text-indent:20px;'>In this work, we provide a result on the derivation of the incompressible Navier-Stokes-Fourier system from the Landau equation for hard, Maxwellian and moderately soft potentials. To this end, we first investigate the Cauchy theory associated to the rescaled Landau equation for small initial data. Our approach is based on proving estimates of some adapted Sobolev norms of the solution that are uniform in the Knudsen number. These uniform estimates also allow us to obtain a result of weak convergence towards the fluid limit system.</p>

41

Li, Sai, and Yang Li. "Incompressible limit on thin domains with periodic boundary condition." Nonlinearity 34, no. 9 (July 29, 2021): 6273–300. http://dx.doi.org/10.1088/1361-6544/ac14a0.

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42

Rossow, Cord-Christian. "Extension of a Compressible Code Toward the Incompressible Limit." AIAA Journal 41, no. 12 (December 2003): 2379–86. http://dx.doi.org/10.2514/2.6863.

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43

Le Dret, H. "Incompressible limit behaviour of slightly compressible nonlinear elastic materials." ESAIM: Mathematical Modelling and Numerical Analysis 20, no. 2 (1986): 315–40. http://dx.doi.org/10.1051/m2an/1986200203151.

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44

Masmoudi, Nader. "Incompressible, inviscid limit of the compressible Navier–Stokes system." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 18, no. 2 (March 2001): 199–224. http://dx.doi.org/10.1016/s0294-1449(00)00123-2.

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45

Ding, Shijin, Jinrui Huang, Huanyao Wen, and Ruizhao Zi. "Incompressible limit of the compressible nematic liquid crystal flow." Journal of Functional Analysis 264, no. 7 (April 2013): 1711–56. http://dx.doi.org/10.1016/j.jfa.2013.01.011.

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46

Kelliher, James P. "Expanding Domain Limit for Incompressible Fluids in the Plane." Communications in Mathematical Physics 278, no. 3 (November 24, 2007): 753–73. http://dx.doi.org/10.1007/s00220-007-0388-y.

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47

Secchi, P. "On the Singular Incompressible Limit of Inviscid Compressible Fluids." Journal of Mathematical Fluid Mechanics 2, no. 2 (June 2000): 107–25. http://dx.doi.org/10.1007/pl00000948.

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48

Danchin, Raphaël, and Piotr Bogusław Mucha. "Compressible Navier–Stokes system: Large solutions and incompressible limit." Advances in Mathematics 320 (November 2017): 904–25. http://dx.doi.org/10.1016/j.aim.2017.09.025.

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49

Kwon, Young-Sam, and Konstantina Trivisa. "On the incompressible limit problems for multicomponent reactive flows." Quarterly of Applied Mathematics 71, no. 1 (August 27, 2012): 37–67. http://dx.doi.org/10.1090/s0033-569x-2012-01271-6.

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50

Golse, François. "Incompressible hydrodynamics as a limit of the Boltzmann equation." Transport Theory and Statistical Physics 21, no. 4-6 (August 1992): 531–55. http://dx.doi.org/10.1080/00411459208203797.

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