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Quelques problèmes mathématiques en thermodynamique des fluides visqueux et compressibles

Abstract : We present a complete existence theory for the physical system consisting of a viscous compressible fluid and a number of rigid bodies in it. We assume a bounded domain and homogeneous Dirichlet boundary conditions for the velocity. Both the fluid and the bodies are allowed to be heat-conducting and share the heat. The existence of global-in-time variational solutions is proved via the viscosity penalization method due to San Martin, Starovoitov, Tucsnak, whereas the existence theory for a viscous compressible fluid developed by Feireisl is used in the approximations as well as in the last high-viscosity limit. The second subject is an improvement of the existence theory for steady barotropic ows. We use L1 estimates for the inverse Laplacian of the pressure introduced by Plotnikov,Sokolowski and Frehse, Goj, Steinhauer together with the non-linear potential theory due to Adams and Hedberg, to get a priori estimates and to prove existence of weak solutions
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Submitted on : Tuesday, January 5, 2010 - 10:22:19 AM
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Jan Brezina. Quelques problèmes mathématiques en thermodynamique des fluides visqueux et compressibles. Dynamique des Fluides [physics.flu-dyn]. Université du Sud Toulon Var, 2008. Français. ⟨tel-00443927⟩

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