Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces

Abstract

In this paper, we study the blowup of the $N$-dim Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. We provide a novel integration method to show that the non-trivial classical solutions $(\rho ,V)$, with compact support in $[0,R]$, where $R>0$ is a positive constant and in the sense which $\rho (t,r)=0$ and $V(t,r)=0$ for $r\ge R$, under the initial condition% $H_0={\int }_0^{R}r{V}_{0}dr>0$ blow up on or before the finite time $T=R^3/(2H_0)$ for pressureless fluids or $\gamma >1.$ The main contribution of this article provides the blowup results of the Euler $(\delta =0)$ or Euler-Poisson $(\delta =1)$ equations with repulsive forces, and with pressure $(\gamma >1)$, as the previous blowup papers (\cite{MUK} \cite{MP}, \cite{P} and \cite{CT}) cannot handle the systems with the pressure term, for $C^1$ solutions.

Accepted by Nonlinear Analysis Series A: Theory, Methods & Applications Key Words: Euler Equations, Euler-Poisson Equations, Integration Method, Blowup, Repulsive Forces, With Pressure, $C^1$ Solutions, No-Slip Condition

References in corpus (4)

• Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars
• Some Exact Blowup Solutions to the Pressureless Euler Equations in R^N
• Euler-Poisson-Newton approach in Cosmology
• Analytical Blowup Solutions to the Isothermal Euler-Poisson Equations of Gaseous Stars in R^N

Cited by in corpus (5)

• Blow-up Phenomena for Compressible Euler Equations with Non-vacuum Initial Data
• Blowup for the C^1 Solutions of the Euler-Poisson Equations of Gaseous Stars in R^N
• Blowup of Regular Solutions for the Relativistic Euler-Poisson Equations
• Existence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinement
• Blowup for $C^2$ Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology