Communications in Mathematical Sciences

Volume 20 (2022)

Number 6

Nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising from radiation hydrodynamics

Pages: 1637 – 1657

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n6.a8

Authors

Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Yongkai Liao (Center for Math. Sciences, China University of Geosciences, Wuhan, China; School of Math. and Physics, China University of Geosciences, Wuhan, China; and Laboratory of Comp. Physics, Institute of Applied Physics & Comp. Math., Beijing, China)

Abstract

We prove rigorously the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising in radiation hydrodynamics. For sufficiently well-prepared initial data, we obtain the uniform estimates of smooth solutions and establish the convergence of the model to the Euler system coupled with a nonlinear diffusion equation.

Keywords

diffusion limit, nonequilibrium regime, radiation hydrodynamics, Euler-P1 approximation

2010 Mathematics Subject Classification

35D35, 35Q31, 35Q35

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This research is supported by the National Natural Science Foundation of China (Grant No. 12131007 and 12071044) and ISF-NSFC joint research program (Grant No.11761141008). The research of Yongkai Liao is supported by National Natural Science Foundation of China (Grant No. 12101579), Foundation of LCP (Grant No. 6142A05Q2020-001), and the Natural Science Foundation of Hubei Province, China (Grant No. 2021CFB022).

Received 11 May 2021

Received revised 11 October 2021

Accepted 17 January 2022

Published 14 September 2022