Global well-posedness and large time behavior of classical solutions to the diffusion approximation model in radiation hydrodynamics

Peng Jiang

doi:10.3934/dcds.2017087

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2017, Volume 37, Issue 4: 2045-2063. Doi: 10.3934/dcds.2017087

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Global well-posedness and large time behavior of classical solutions to the diffusion approximation model in radiation hydrodynamics

Peng Jiang^1,2,

1.
Department of Mathematics, College of Science, Hohai University, Nanjing 210098, China
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received: May 2016

Revised: November 2016

Published: May 2017

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Abstract

We are concerned with the global well-posedness of the diffusion approximation model in radiation hydrodynamics, which describe the compressible fluid dynamics taking into account the radiation effect under the non-local thermal equilibrium case. The model consist of the compressible Navier-Stokes equations coupled with the radiative transport equation with non-local terms. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The existence of global solution is proved based on the classical energy estimates, which are considerably complicated and some new ideas and techniques are thus required. Moreover, it is shown that neither shock waves nor vacuum and concentration in the solution are developed in a finite time although there is a complex interaction between photons and matter.

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Mathematics Subject Classification: 76N10, 78A40.

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