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

Full Text (PDF format)

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