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arXiv · 1909.05683

Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping

Yuusuke Sugiyama
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Abstract

In this paper, we consider the 1D compressible Euler equation with the damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu <1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, 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.

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Yuusuke Sugiyama. 2019-09-11. Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping. https://arxiv.org/abs/1909.05683

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