Singularities of solutions to compressible Euler equations with damping

Abstract

In this paper, we study the formation of finite-time singularities of smooth solutions to the compressible Euler equations with damping in arbitrary dimensions for isentropic, polytropic fluid flows. The radial component of initial momentum is assumed to be large enough and the smooth solutions are assumed to be decay at far fields, but it is not required that the initial velocity field has a compact support. It is shown that the smooth solutions to the Cauchy problem will break down in a finite time. Our result partially complements the work for the compactly supported initial velocity field (Sideris et al., 2003).