Stabilities for Euler-Poisson equations with repulsive forces in Rᴺ

This article extends the previous paper (M.W. Yuen, Stabilities for Euler-Poisson Equations in Some Special Dimensions, J. Math. Anal. Appl. 344(2008), 145–156) from the Euler-Poisson equations for at-tractive forces to the repulsive ones in Rᴺ (N≥2). The similar stabilities of the system are studied. We also explain that it is impossible to have density collapsing solutions with compact support from classical solutions for a system with repulsive forces for ƴ>1. Copyright © 2013 Manwai Yuen.