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

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 $\lambda \in (\frac{1}{7},1)$. 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.

References in corpus (2)

• Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions
• $L^1$-convergence to generalized Barenblatt solution for compressible Euler equations with time-dependent damping