Дисертації з теми "Navier Stoke"
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Maidana, Manuel Augusto. "Desarrollo de un modelo numérico 3D en elementos finitos para las ecuaciones de Navier-Stokes : aplicaciones oceanográficas." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/457520.
Повний текст джерелаIn this thesis finite element model was developed, named HELIKE, for the numerical simulation of the three-dimensional, turbulent, non-hydrostatic, free-surface flows like those arising in the study of the motion of water in coastal regions. The kinematic free-surface equation is used to compute the surface elevation, without resorting to vertical averages. The model developed here incorporates surface wind stress, bottom friction, Coriolis acceleration, the baroclinic term to take account the density gradients, and it is applicable to irregular bottom topographies. A pressure stabilization technique is employed to stabilize the finite element solution. Numerical results confirm the accuracy, robustness and applicability of the proposed method.
Ghosh, Amrita. "Naviers-Stokes equations with Navier boundary condition." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3021/document.
Повний текст джерелаMy PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up
GALLANA, LUCA. "Statistical analysis of inhomogeneous fluctuation fields. Scalar transport in shearless turbulent mixing, effects of stratification, solar wind and solar wind-interstellar medium interaction." Doctoral thesis, Politecnico di Torino, 2016. http://hdl.handle.net/11583/2653026.
Повний текст джерелаCai, Zhemin. "A High-order Discontinuous Galerkin Method for Simulating Incompressible Fluid-Thermal-Structural Problems." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/20961.
Повний текст джерелаBORDIGNON, ALEX LAIER. "NAVIER-STOKES EM GPU." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8928@1.
Повний текст джерелаNesse trabalho, mostramos como simular um fluido em duas dimensões em um domÃnio com fronteiras arbitrárias. Nosso trabalho é baseado no esquema stable fluids desenvolvido por Joe Stam. A implementação é feita na GPU (Graphics Processing Unit), permitindo velocidade de interação com o fluido. Fazemos uso da linguagem Cg (C for Graphics), desenvolvida pela companhia NVidia. Nossas principais contribuições são o tratamento das múltiplas fronteiras, onde aplicamos interpolação bilinear para atingir melhores resultados, armazenamento das condições de fronteira usa apenas um canal de textura, e o uso de confinamento de vorticidade.
In this work we show how to simulate fluids in two dimensions in a domain with arbitrary bondaries. Our work is based on the stable fluid scheme developed by Jo Stam. The implementation is done in GPU (Graphics Processinfg Unit), thus allowing fluid interaction speed. We use the language Cg (C for Graphics) developed by the company Nvídia. Our main contributions are the treatment of domains with multiple boundaries, where we apply bilinear interpolation to obtain better results, the storage of the bondaty conditions in a unique texturre channel, and the use of vorticity confinement.
Rejaiba, Ahmed. "Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3050/document.
Повний текст джерелаThis thesis is devoted to the study of the Stokes equations and Navier-Stokes equations with Navier boundary conditions in a bounded domain of . The work contains three chapters: In the first chapter, we consider the stationary Stokes equations with Navier boundary condition. We show the existence, uniqueness and regularity of the solution in the Hilbert case and in the -theory. We prove also the case of very weak solutions. In the second chapter, we focus on the Navier-Stokes equations with the Navier boundary condition. We show the existence of the weak solution in , with by a fixed point theorem over the Oseen equation. We show also the existence of the strong solution in . In chapter three, we study the evolution Stokes problem with Navier boundary condition. For this, we apply the analytic semi-groups theory, which plays a crucial role in the study of existence and uniqueness of solution in the case of the homogeneous evolution problem. We treat the case of non-homogeneous problem through imaginary powers of the Stokes operator
Cannone, Marco. "Ondelettes, paraproduits et Navier-Stokes." Paris 9, 1994. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1994PA090016.
Повний текст джерелаMallinger, François. "Couplage adaptatif Boltzmann Navier-Stokes." Paris 9, 1996. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1996PA090042.
Повний текст джерелаWe study external flows for semirarefied régimes at high mach number. We propose a domain décomposition strategy coupling Boltzmann and Navier-Stokes models. The coupling is done by boundary conditions. The Boltzmann and Navier-Stokes computational domains are defined automatically thanks to a critérium analysing the validity of the numerical Navier-Stokes solution. We propose therefore an adaptative coupling algorithm taking into account both the automatic définition of the computation domains and a time marching algorithm to couple the models. The whole strategy results from the transition between the microscopie model (Boltzmann) and the macroscopie model (Navier-Stokes). In order to generalize this adaptative coupling, we study this connection for diatomic gases. Finally, we justify the coupled problem from a mathematical view point
Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.
Повний текст джерелаLandmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds averaged Navier-Stokes equations." München Verl. Dr. Hut, 2007. http://d-nb.info/988422433/04.
Повний текст джерелаBenson, D. J. A. "Finite volume solution of Stokes and Navier-Stokes equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302883.
Повний текст джерелаAllaire, Grégoire. "Homogénéisation des équations de Stokes et de Navier-Stokes." Paris 6, 1989. http://www.theses.fr/1989PA066010.
Повний текст джерелаSahin, Pinar. "Navier-stokes Calculations Over Swept Wings." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607618/index.pdf.
Повний текст джерелаShuttleworth, Robert. "Block preconditioning the Navier-Stokes equations." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7002.
Повний текст джерелаThesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Gwilliam, Catherine Sarah. "Parallel algorithms for Navier-Stokes modelling." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357478.
Повний текст джерелаLysov, Vyacheslav. "From Petrov-Einstein to Navier-Stokes." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11656.
Повний текст джерелаPhysics
Neklyudov, Mikhail. "Navier-Stokes equations and vector advection." Thesis, University of York, 2006. http://etheses.whiterose.ac.uk/11011/.
Повний текст джерелаPatni, Kavita. "Damped Navier-Stokes equation in 2D." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/809731/.
Повний текст джерелаAlbanez, Débora Aparecida Francisco 1984. "Continuous data assimilation for Navier-Stokes-alpha model = Assimilação contínua de dados para o modelo Navier-Stokes-alpha." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306185.
Повний текст джерелаTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-25T00:41:15Z (GMT). No. of bitstreams: 1 Albanez_DeboraAparecidaFrancisco_D.pdf: 3117782 bytes, checksum: 4f8e30c3d217ed3a6d26e9924d4df7ab (MD5) Previous issue date: 2014
Resumo: Motivados pela existênca de um número finito de parâmetros determinantes (graus de liberdade), tais como modos, nós e médias espaciais locais para sistemas dinâmicos dissipativos, principalmente as equações de Navier-Stokes, apresentamos nesta tese um novo algoritmo de assimilação contínua de dados para o modelo tridimensional das equações Navier-Stokes-alpha, o qual consiste na introdução de um tipo geral de operador interpolante de aproximação (construído a partir de medições observacionais) dentro das equações de Navier-Stokes-alpha. O principal resultado garante condições sob a resolução espacial de dimensão finita dos dados coletados, suficientes para que a solução aproximada, construída a partir desses dados coletados, convirja para a referente solução que não conhecemos (realidade física) no tempo. Essas condições são dadas em termos de alguns parâmetros físicos, tais como a viscosidade cinemática, o tamanho do domínio e o termo de força
Abstract: Motivated by the presence of the finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, specially Navier-Stokes equations, we present in this thesis a new continuous data assimilation algorithm for the three-dimensional Navier-Stokes-alpha model, which consists of introducing a general type of approximation interpolation operator, (that is constructed from observational measurements), into the Navier-Stokes-alpha equations. The main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkwown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of the domain and the forcing term
Doutorado
Matematica
Doutora em Matemática
Tryggeson, Henrik. "Analytical vortex solutions to Navier-Stokes equation." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1282.
Повний текст джерелаInubushi, Masanobu. "Covariant Lyapunov Analysis of Navier-Stokes Turbulence." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/175095.
Повний текст джерелаAl-Jaboori, Mustafa Ali Hussain. "Navier-Stokes equations on the β-plane". Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5582/.
Повний текст джерелаNgom, Evrad Marie Diokel. "Contrôle frontière des équations de Navier-Stokes." Phd thesis, Université Claude Bernard - Lyon I, 2014. http://tel.archives-ouvertes.fr/tel-01064942.
Повний текст джерелаHaddon, E. W. "Numerical studies of the Navier-Stokes equations." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377745.
Повний текст джерелаTang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.
Повний текст джерелаHachicha, Imène. "Approximations hyperboliques des équations de Navier-Stokes." Thesis, Evry-Val d'Essonne, 2013. http://www.theses.fr/2013EVRY0015/document.
Повний текст джерелаIn this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one
Słomka, Jonasz. "Generalized Navier-Stokes equations for active turbulence." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117861.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 211-227).
Recent experiments show that active fluids stirred by swimming bacteria or ATPpowered microtubule networks can exhibit complex flow dynamics and emergent pattern scale selection. Here, I will investigate a simplified phenomenological approach to 'active turbulence', a chaotic non-equilibrium steady-state in which the solvent flow develops a dominant vortex size. This approach generalizes the incompressible Navier-Stokes equations by accounting for active stresses through a linear instability mechanism, in contrast to externally driven classical turbulence. This minimal model can reproduce experimentally observed velocity statistics and is analytically tractable in planar and curved geometry. Exact stationary bulk solutions include Abrikosovtype vortex lattices in 2D and chiral Beltrami fields in 3D. Numerical simulations for a plane Couette shear geometry predict a low viscosity phase mediated by stress defects, in qualitative agreement with recent experiments on bacterial suspensions. Considering the active analog of Stokes' second problem, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. The model readily generalizes to curved geometries. On a two-sphere, we present exact stationary solutions and predict a new type of upward energy transfer mechanism realized through the formation of vortex chains, rather than the merging of vortices, as expected from classical 2D turbulence. In 3D simulations on periodic domains, we observe spontaneous mirror-symmetry breaking realized through Beltrami-like flows, which give rise to upward energy transfer, in contrast to the classical direct Richardson cascade. Our analysis of triadic interactions supports this numerical prediction by establishing an analogy with forced rigid body dynamics and reveals a previously unknown triad invariant for classical turbulence.
by Jonasz Słomka.
Ph. D.
Silva, Felipe Wallison Chaves. "Controlabilidade para o sistema de Navier-Stokes." Universidade Federal da Paraíba, 2009. http://tede.biblioteca.ufpb.br:8080/handle/tede/7452.
Повний текст джерелаCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Cook's local infuence approach based on normal curvature is an important diagnostic tool for assessing local infuence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of infuence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a diferential-geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model.
Esta dissertação é dedicada ao estudo do sistema de Navier-Stokes sob ponto de vista da teoria do controle. Primeiramente estudamos a controlabilidade das aproximações de Galerkin do sistema de Navier-Stokes. Utilizando argumentos de dualidade e de ponto fixo, mostramos que, com hipóteses adequadas sobre a base de Galerkin, estas aproximações, finito dimensionais, são exatamente controláveis. Passando ao modelo em dimensão infinita, analisamos a controlabilidade sobre trajetórias. Isto é feito usando uma desigualdade do tipo Calerman para o sistema de Navier-Stokes linearizado e uma versão do teorema da função inversa. Dessa forma, temos um resultado de controlabilidade local exata para o sistema de Navier-Stokes.
Drouet, Aurélien. "Apports de la résolution multi-blocs pour la simulation de la manoeuvrabilité des sous-marins et des bâtiments de surface." Ecole centrale de Nantes, 2011. http://www.theses.fr/2011ECDN0045.
Повний текст джерелаEstimating the performances of ship maneuverability is a necessary stage to guarantee the safety of the crew and of the surrounding environment. The objective of this PhD thesis is to adapt a free surface Navier-Stokes computational code in order to be used for a submarine or ship maneuverability modeling. The first chapters are dedicated to the definition of Navier-Stockes equations and their linearization and discretization that are used for the numerical scheme. Then, a brief chapter presents the different mesh topologies and advantages of using the multi-block meshing approach. The developments implemented into the code to take into account this innovating meshing topology are presented, as well as a the associated validation test cases. The overall functionabilities needed for an auto-propulled maneuvering ship are then detailed. The CPU time must be relatively low since the numerical code is dedicated to an industrial use. Hence, a description of optimization and parallelization stages performed on the initial single-block code is described. To conlude, the two last chapters present a validation test case end possible industrial applications enable by the developments performed. The validation test case is performes on a submarine (DARPA SUBOFF) on a wide range of fixed model configurations, and results are compared to experimental hydrdynamic coefficient. Possible configurations of submarine or ship maneuverability in auto-propolled and free model configurations are presented, such as turning cricle maneuver, pullout, zigzag. .
De, Santis Dante. "Schémas d'ordre élevé distribuant le résidu pour la résolution des équations de Navier-Stokes et Navier-Stokes moyennées (RANS)." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00935419.
Повний текст джерелаBarrère, Jean. "Modélisation des écoulements de Stokes et Navier-Stokes en milieux poreux." Bordeaux 1, 1990. http://www.theses.fr/1990BOR10516.
Повний текст джерелаWachsmuth, Daniel. "Optimal control of the unsteady Navier-Stokes equations." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982143419.
Повний текст джерелаJiang, Ning. "Weakly compressible Navier-Stokes approximation of gas dynamics." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3883.
Повний текст джерелаThesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Liu, Jie. "A class of efficient, stable Navier-Stokes solvers." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3695.
Повний текст джерелаThesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.
Повний текст джерелаGrira, Sofiane. "Les équations de Navier-Stokes nonlinéaires dans IR³." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ26576.pdf.
Повний текст джерелаLi, Ming. "Numerical solutions for the incompressible Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0016/NQ37725.pdf.
Повний текст джерелаLitton, Daniel. "Algorithmic Enhancements to the VULCAN Navier-Stokes Solver." NCSU, 2003. http://www.lib.ncsu.edu/theses/available/etd-08132003-230354/.
Повний текст джерелаSommerville, Lesley Laverne. "A Parabolized navier-stokes model for static mixers." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/19535.
Повний текст джерелаLi, Yuhong. "Asymptotical behaviour of 2D stochastic Navier-Stokes equations." Thesis, University of Hull, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411901.
Повний текст джерелаOsborne, Daniel. "Navier-Stokes equations and stochastic models of turbulence." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497064.
Повний текст джерелаRyou, H. S. "Viscous/inviscid matching using imbedded Navier/Stokes equations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47236.
Повний текст джерелаSchäfer, Christian Thomas. "Elastohydrodynamic lubrication based on the Navier-Stokes equations." Thesis, Liverpool John Moores University, 2005. http://researchonline.ljmu.ac.uk/5788/.
Повний текст джерелаNewman, Christopher K. "Exponential Integrators for the Incompressible Navier-Stokes Equations." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/29340.
Повний текст джерелаPh. D.
Zahed, Hanadi. "Computation of bifurcations for the Navier-Stokes equations." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/computation-of-bifurcations-for-the-navierstokes-equations(6f5f55ac-0379-495b-8652-7baaeb117a4b).html.
Повний текст джерелаMontoya, Zambrano Cristhian David. "Inverse source problems and controllability for the stokes and navier-stokes equations." Tesis, Universidad de Chile, 2016. http://repositorio.uchile.cl/handle/2250/141346.
Повний текст джерелаThis thesis is focused on the Navier{Stokes system for incompressible uids with either Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some ideas in the context of the control theory and inverse source problems. The thesis is divided in three parts. In the rst part, we deal with the local null controllability for the Navier{Stokes system with nonlinear Navier{slip conditions, where the internal controls have one vanishing component. The novelty of the boundary conditions and the new estimates with respect to the pressure term, has allowed us to extend previous results on controllability for the Navier{ Stokes system. The main ingredients to build our result are the following: a new regularity result for the linearized system around the origin, and a suitable Carleman inequality for the adjoint system associated to the linearized system. Finally, xed point arguments are used in order to conclude the proof. In the second part, we deal with an inverse source problem for the N- dimensional Stokes system from local and missing velocity measurements. More precisely, our main result establishes a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function, meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable Sobolev space. The main tools are the following: connection between null controllability and inverse problems throughout a result on null controllability for the N- dimensional Stokes system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral equations. We also implement this result and present several numerical experiments that show the feasibility of the proposed recovering formula. Finally, the last chapter of the thesis presents a partial result of stability for the Stokes system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for solving inverse problems and some topics in degenerate Sobolev spaces.
Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.
Повний текст джерелаAl, Baba Hind. "Théorie des semi-groupes pour les équations de Stokes et de Navier-Stokes avec des conditions aux limites de type Navier." Thesis, Pau, 2015. http://www.theses.fr/2015PAUU3008/document.
Повний текст джерелаThis thesis is devoted to the mathematical theoretical study of the Stokes and Navier-Stokes equations in a bounded domain of R^3 using the semi-group theory. Three different types of boundary conditions will be considered: Navier boundary conditions, Navier-type boundary conditions and boundary condition involving the pressure. This manuscript contains six chapters. We prove first the analyticity of the Stokes semi-group with each of the boundary conditions stated above. This allows us to solve the time dependent Stokes problem using the semi-group theory. We will study also the complex and fractional powers of the Stokes operator for which we prove some properties and estimations. These results will be used in the sequel to prove an estimate of type L^p-L^q for the Stokes semigroup, as well as the maximal L^p-L^q regularity for the inhomogeneous Stokes problem and an existence result for the non-linear problem. Next we study the time dependent Stokes problem, besides the maximal L^p-L^q regularity, we prove the existence of weak u∈L^q (0,T; W^(1,p) (Ω)), strong u∈L^q (0,T; W^(2,p) (Ω)) and very weak u∈L^q (0,T; L^p (Ω)) solutions to the Stokes problem. We end with the study of the Navier-Stokes problem. First using the L^p-L^q estimate for the Stokes semi-group we prove the existence of a unique local in time mild solution for the Navier-Stokes problem that verifies u∈BC([0,T_0 ); L_(σ,τ)^p (Ω))∩L^q (0,T_0; L_(σ,τ)^r (Ω)), q,r>p, 2/q+3/r=3/p.Furthermore, for some initial data the solution is global in time. Finally, by estimating the non-linear term as a function of the fractional powers of the Stokes operator we prove that the solution is regular
Guzzo, Sandro Marcos. "Estudo de equações do tipo Navier-Stokes com retardo." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01092009-105829/.
Повний текст джерелаIn this work we stuy the existence of solutions for a Navier-Stokes typt equations with delay in the external force and in the nonlinear term. Using the semi-group theory we study the existence of solution for a problem in the form \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), ijn \'OMEGA\' x (0, T), div u(t) = 0 in \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x \'IT BELONGS \' OMEGA\', u(t, x) = 0 t > 0, X \'IT BELONGS\' \'PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'IT BELONGS\' (- \'INFINITY\', 0) x \'IT BELONGS\' \'OMEGA\', where F(t, \'u .t) = INT.IND.t SUP. -\' INFINITY\' \' ALFA(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITY \'BETA\' (s-t)u(s)ds. On another hand using the Galerkin appreoximations method we study the same with F(.) e g(.) given by f(t; \'u INDS.t\') = u(t-r(t)); and g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), for some G appropriated. In thiis case, we study also the stability of stanionary solutions
Yung, Hoi Yan Ada, and 翁凱欣. "On block preconditioners for the incompressible Navier-Stokes equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44907138.
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