Singularities of solutions to compressible Euler equations with vacuum
Analysis of PDEs
2012-03-23 v2
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 , but not required to have a compact support. It is shown that the norm of the velocity field and the sound speed will blow up in a finite time.
Cite
@article{arxiv.1203.2396,
title = {Singularities of solutions to compressible Euler equations with vacuum},
author = {Zhen Lei and Yi Du and Qingtian Zhang},
journal= {arXiv preprint arXiv:1203.2396},
year = {2012}
}
Comments
The initial velocity has no compact support, and the initial density allows vacuum