Singularities of solutions to compressible Euler equations with vacuum

2012/03/12 by Lei, Zhen, Du, Yi, Zhang, Qingtian
#35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.2396

Abstract

Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be symmetric and the initial sound speed is required to vanish at the origin. They are smooth in Sobolev space H³, but not required to have a compact support. It is shown that the H³ norm of the velocity field and the sound speed will blow up in a finite time.

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