Decay of a model system of radiating gas

Abstract

This paper is concerned with optimal time-decay estimates of solutions of the Cauchy problem to a model system of the radiating gas in ${\mathbb{R}}^n$. Compared to Liu and Kawashima (2011) \cite{Liu1} and Wang and Wang (2009) \cite{Wang}, without smallness assumption of initial perturbation in $L^1$-norm, we study large time behavior of small amplitude classical solutions to the Cauchy problem. The optimal $H^N$-norm time-decay rates of the solutions in ${\mathbb{R}}^n$ with $1\le n\le 4$ are obtained by applying the Fourier splitting method introduced in Schonbek (1980) \cite{Schonbek1} with a slight modification and an energy method. Furthermore, basing on a refined pure energy method introduced in Guo and Wang \cite{Guo} (2011), we give optimal $L^p$-$L^2({\mathbb{R}}^3)$ decay estimates of the derivatives of solutions when initial perturbation is bounded in $L^p$-norm with some $p\in (1,2]$.

15 pages

References in corpus (2)

• Shock Profiles for Non Equilibrium Radiating Gases
• Stability of radiative shock profiles for hyperbolic-elliptic coupled systems