The time‐asymptotic expansion for the compressible Euler equations with damping-Reference-Cited by-同舟云学术

The time‐asymptotic expansion for the compressible Euler equations with damping

Published:2024-04-30 Issue:5 Volume:109 Page:
ISSN:0024-6107
Container-title:Journal of the London Mathematical Society
language:en
Short-container-title:Journal of London Math Soc

Author:

Huang Feimin¹²,Wu Xiaochun³

Affiliation:

1. Academy of Mathematics and systems Science Chinese Academy of Sciences Beijing China

2. School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China

3. School of Mathematics and Statistics, HNP‐LAMA Central South University Changsha China

Abstract

AbstractIn 1992, Hsiao and Liu first showed that the solution to the compressible Euler equations with damping time‐asymptotically converges to the diffusion wave of the porous media equation. Geng et al. proposed a time‐asymptotic expansion around the diffusion wave , which is a better asymptotic profile than . In this paper, we rigorously justify the time‐asymptotic expansion by the approximate Green function method and the energy estimates. Moreover, the large time behavior of the solution to compressible Euler equations with damping is accurately characterized by the time‐asymptotic expansion.

Funder

National Key Research and Development Program of China

National Natural Science Foundation of China

Publisher

Wiley

Link

https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/jlms.12908

Reference31 articles.

1. Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping

2. A class of similarity solutions of the nonlinear diffusion equation

3. L1-convergence rates to the Barenblatt solution for the damped compressible Euler equations

4. The time asymptotic expansion for the compressible Euler equations with time-dependent damping

5. $L^1$-Convergence to Generalized Barenblatt Solution for Compressible Euler Equations with Time-Dependent Damping