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VOL. 85 | 2020 Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping
Yuusuke Sugiyama

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

## Abstract

In this paper, we consider the 1D compressible Euler equation with the damping coefficient $\lambda/(1 + t)^{\mu}$. Under the assumption that $0 \leq \mu \lt 1$ and $\lambda \gt 0$ or $\mu = 1$ and $\lambda \gt 2$, we prove that solutions exist globally in time, if initial data are small $C^1$ perturbation near constant states. In particular, we remove the conditions on the limit $\lim_{|x| \rightarrow \infty} (u (0,x), v (0,x))$, assumed in previous results.

## Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510379

Subjects:
Primary: 35Q31
Secondary: 35A01, 35L40