Global existence to the equilibrium diffusion model in radiative hydrodynamics

Thierry Goudon 1, 2, 3 Chunjin Lin 4
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.
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https://hal.inria.fr/hal-00905333
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Submitted on : Monday, November 18, 2013 - 10:18:46 AM
Last modification on : Tuesday, July 3, 2018 - 11:43:24 AM

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Thierry Goudon, Chunjin Lin. Global existence to the equilibrium diffusion model in radiative hydrodynamics. Chinese Annals of Mathematics - Series B, Springer Verlag, 2011, 32 (4), pp.549--568. ⟨10.1007/s11401-011-0658-z⟩. ⟨hal-00905333⟩

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