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arXiv · 2202.13385

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

Shifeng Geng·Feimin Huang·Guanghui Jin·Xiaochun Wu
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Abstract

In this paper, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $\lambda \in (\frac17,1)$. In other word, instead of the self-similar solution of GPME, the expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping.

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Shifeng Geng, Feimin Huang, Guanghui Jin, Xiaochun Wu. 2022-02-27. The time asymptotic expansion for the compressible Euler equations with time-dependent damping. https://doi.org/10.1088/1361-6544/acecf6

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