Singularities of solutions to compressible Euler equations with vacuum

Details Singularities of solutions to compressible Euler equations with vacuum Singularities of solutions to compressible Euler equations with vacuum

2012-03-12

arxiv.org/abs/1203.2396v2

Mathematics

Analysis of PDEs

The initial velocity has no compact support, and the initial density allows vacuum

Scientific paper

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 $H^3$, but not required to have a compact support. It is shown that the $H^3$ norm of the velocity field and the sound speed will blow up in a finite time.

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