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

2010/12/23 by Yuen, Manwai
#35B30 #35B44 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1012.5143

Abstract

In this paper, we continue to study the blowup problem of the N-dimensional compressible Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. In details, we extend the recent result of "M.W. Yuen, Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces, Nonlinear Analysis Series A: Theory, Methods & Applications 74 (2011), 1465--1470.". We could further apply the integration method to obtain the more general results which the non-trivial classical solutions (ρ,V), with compact support in [0,R], where R>0 is a positive constant with ρ(t,r)=0 and V(t,r)=0 for r≥ R, under the initial condition% H₀=∫₀^RrⁿV₀drgt;0 where an arbitrary constant n>0, blow up on or before the finite time T=2Rⁿ⁺²/(n(n+1)H₀) for pressureless fluids or γ>1. The results obtained here fully cover the previous known case for n=1.

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