Orientador: Jose Luiz Boldrini / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-19T02:31:13Z (GMT). No. of bitstreams: 1 LorcaPizarro_SebastianAntonio_D.pdf: 1280091 bytes, checksum: 7d515274b16d8ac09d18f4cf718d5213 (MD5) Previous issue date: 1994 / Resumo: Não informado / Abstract: Not informed / Doutorado / Doutor em Matemática

Orientador: Jose Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-19T11:10:15Z (GMT). No. of bitstreams: 1 Torres_ElvaElianaOrtega_M.pdf: 2648095 bytes, checksum: 363ebe5e7a7d277dc6b22c4a8392c5ed (MD5) Previous issue date: 1994 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática Aplicada

Many interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.

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Les équations fondamentales décrivant la dynamique de l'océan sont en théorie les équations de Navier-Stokes sur une sphère en rotation, auxquelles il faut a jouter une équation d'état pour la densité, et des équations de transport-diffusion pour les traceurs. Toutefois, un certain nombre de considérations physiques et de limitations pratiques ont nécessité le développement de modèles plus simples. En effet, un certain nombre d'hypothèses simplificatrices sont pleinement justifiées du point de vue de la physique des mouvements océaniques, dont les principales sont les approximations de couche mince et de Boussinesq. D'autre part, étant donné les dimensions des bassins océaniques (plusieurs centaines à plusieurs milliers de kilomètres), les coûts de calculs sont un facteur pratique extrêmement limitant. On est, à l'heure actuelle, capable de simuler l'océan mondial avec une résolution de l'ordre de dix kilomètres, en utilisant des modèles dits aux équations primitives, dont le coût de calcul est bien inférieur à celui des équations de Navier-Stokes. On est donc bien loin d'une modélisation complète des phénomènes décrits par ces équations, qui nécessiterait en théorie de considérer des échelles de l'ordre du millimètre. Les équations primitives sont issues des équations complètes de la mécanique des fluides en effectuant l'approximation hydrostatique, justifiée par la faible profondeur des domaines considérés au regard de leur dimension horizontale. Dans cette thèse, nous considérerons les équations de Navier-Stokes (NS) qui sont le coeur du modèle complet évoqué ci-dessus, sans prendre en compte les équations de la densité et des traceurs (salinité, température, etc.). Nous utiliserons l'approximation hydrostatique dans le chapitre 10, et le modèle sera naturellement appelé Navier-Stokes hydrostatique (NSH). Il correspond aux équations primitives dans lesquelles on ne prendrait pas en compte la densité et les traceurs. C'est dans ce cadre que se situe le travail présenté dans cette thèse, avec l'objectif à moyen terme de pouvoir coupler de façon rigoureuse et efficace les équations de Navier-Stokes avec les équations primitives. Dans une première partie, on présentera quelques rappels sur les équations de Navier-Stokes, leur discrétisation, ainsi que le cas-test de la cavité entraînée qui sera utilisé dans tout ce document. Dans une deuxième partie, on met en œuvre les méthodes de Schwarz sur les équations de Stokes et Navier-Stokes, en dérivant notamment des conditions absorbantes exactes et approchées pour ces systèmes. Enfin, dans une troisième partie, on proposera des pistes vers le couplage Navier-Stokes/Navier-Stokes hydrostatique décrit ci-dessus. / Fundamental equations describing the ocean dynamic are theoretically Navier-Stokes equations over a rotating sphere, whom need to add a state equation for the fluid density, and advection-diffusion equations for tracers. However, some physical considerations and practical limitations required to developped more simple models. Indeed, some simplifying hypotheses are well justified from a ocean dynamic point of view, whose principal ones are thin layer and Boussinesq approximations. On the other hand, considering the dimensions of oceans (from serveral hundreds to serveral thousands kilometers), computations costs are a very practical limitating factor. We are, by now, able to simulate the global ocean with about ten kilometers large grid mesh. This is very far from a complete modelisation of all phenomenes decribed by the Navier-Stokes equations, which require to consider scales of milimeters order. Primitives equations derive from complete equations describing fluid mecanics, by doing the hydrostatic approximations, which is justified by the low deepness of considered domains with regard to their horizontal dimension. In this thesis, we are considering Navier-Stokes equations (NS) which are the heart of the complete modele mentionned previously, without holding in account density and tracers equations. We will use the hydrostatic approximations, and the resulting equations will be named as hydrostatic Navier-Stokes equations (NSH).The mid term objective is to couple carefully Navier-Stokes equations with primitive equation. In a first part, we will remind few results for Navier-Stokes equations, their discretization, and the lid-driven cavity which wil be used as a test-case. In a second part, we will use Schwarz method with Stokes and Navier-Stokes equations, deriving in particular exact and approched absorbing interface conditions for these systems. Finally, in a third part, we shall propose first results towards coupling Navier-Stokes and hydrostatic Navier-Stokes equations.

Next, we consider that the fluids are isentropic and the domain is also bounded, smooth, simply connected in R2 . We show that the estimates are uniform in all time if the smallness assumption on the initial data is prescribed. It follows that the solutions of compressible Navier-Stokes equations converge to the incompressible ones uniformly in both spatial and temporal variables as the Mach number vanishes. / This thesis deals with the low Mach number limit of the compressible Navier-Stokes equations. It is to verify that the compressible fluids become incompressible as Mach number tends to zero. In another words, the pressure due to compression can be neglected. This is a singular limit. / We will show that, as the Mach number tends to zero, the local smooth solutions of compressible Navier-Stokes equations with zero thermal conductivity coefficient converge strongly to the solutions of incompressible Navier-Stokes equations, provided that the initial data satisfy the "bounded derivative conditions". The key point, which is one of our main contributions, is the uniform high norm estimates in Mach number. We will study two cases. The first case is that, the domain is a finite interval and the boundary condition for the velocity is no-slip. In the second case, the domain is bounded, smooth, and simply connected in R2 . The boundary condition for the velocity is replaced by the slip-type's, thus the vorticity and the divergence of velocity can be estimated separately. / Ou, Yaobin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3546. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Yu, Rongfeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 57-63). / Abstracts in English and Chinese. / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.11 / Chapter 1.1 --- Notations and function spaces --- p.11 / Chapter 1.2 --- Some useful inequalities --- p.12 / Chapter 1.3 --- Fundamental lemmas --- p.15 / Chapter 2 --- Compressible Navier-Stokes Equations for Quantum Fluids --- p.16 / Chapter 2.1 --- Background --- p.17 / Chapter 2.2 --- Derivation of model --- p.17 / Chapter 3 --- Global Weak Solutions to Barotropic Navier-Stokes Equations for Quantum Fluids --- p.22 / Chapter 3.1 --- Reformulation and main results --- p.23 / Chapter 3.2 --- Construction of approximate solutions --- p.27 / Chapter 3.3 --- A priori estimates --- p.39 / Chapter 3.4 --- Proof of Theorem 3.1.6 --- p.40 / Chapter 4 --- Global Existence and Large Time Behavior of Weak Solutions to Quantum Navier-Stokes-Poisson Equa-tions --- p.46 / Chapter 4.1 --- Global existence of weak solutions --- p.47 / Chapter 4.2 --- Large time behavior --- p.50 / Chapter 5 --- Discussions and Future Work --- p.55 / Bibliography --- p.56

Submitted by SABRINA SUELEN AMARAL null (sabrinasuelen_5@hotmail.com) on 2017-02-26T00:34:42Z No. of bitstreams: 1 Dissertação definitiva Sabrina S Amaral - Copia.pdf: 862726 bytes, checksum: ef97a1fa8d86f69f3436915d6d9a433d (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-03-07T13:47:33Z (GMT) No. of bitstreams: 1 amaral_ss_me_sjrp.pdf: 862726 bytes, checksum: ef97a1fa8d86f69f3436915d6d9a433d (MD5) / Made available in DSpace on 2017-03-07T13:47:33Z (GMT). No. of bitstreams: 1 amaral_ss_me_sjrp.pdf: 862726 bytes, checksum: ef97a1fa8d86f69f3436915d6d9a433d (MD5) Previous issue date: 2017-02-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho analisamos as equações de Navier-Stokes em R^n, (n≤3) e mostramos boa colocação global, quando a velocidade inicial pertence ao espaço de Morrey e tem norma suficientemente pequena. Mostramos, também, que se o dado inicial é uma função homogênea de grau -1 então as soluções mild são autossimilares. Além disso, apresentamos um resultado de estabilidade assintótica das soluções mild. / In this work we will analyze the Navier-Stokes equations in R^n, (n≤3) and we will show global well-posedness, when the initial velocity belongs to the Morrey space and with a sufficiently small norm. We will also show that if the initial data is a homogeneous function of degree -1, then the mild solutions are self-similar. Moreover, we will present an asymptotic stability result of the mild solutions.