Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force

Yongcai Geng

doi:10.3934/cpaa.2015.14.549

Article Contents

2015, Volume 14, Issue 2: 549-564. Doi: 10.3934/cpaa.2015.14.549

This issue Previous Article An integral equation involving Bessel potentials on half space Next Article The Liouville type theorem and local regularity results for nonlinear differential and integral systems

Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force

Yongcai Geng^1,

1.
Department of Mathematics, Shanghai Institute of Technology, Shanghai 200235

Received: March 2014

Revised: September 2014

Published: March 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we investigate the singularities formation for the relativistic Euler and Euler-Poisson equations with repulsive force, in spherical symmetry. We will show the non-trivial regular solution $(p^{\frac{\gamma-1}{2\gamma}}\in C^1$) with compact support in $[0,R]$, under a certain condition on initial data \begin{eqnarray} H_0:=\int_0^R rv_0dr>0, \end{eqnarray} will blow up, where $0 < R < \min\{\frac{8}{45},\frac{8(\gamma-1)}{5\gamma+23}\}$ is a constant. Since every term in the relativistic Euler-Poisson equations corresponding to $\rho, v$ in non-relativistic case [34] has a relativistic factor $\frac{1}{\sqrt{1-v^2/c^2}}$, we will separate variables and estimate some integration items instead of direct using integration method as [34].

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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