Improved blowup results for the Euler and Euler–Poisson equations with repulsive forces

Abstract

Some results are presented on the formation of singularities in the solutions of the radially-symmetric N-dimensional Euler or Euler–Poisson equations with repulsive forces. Based on the integration method of M.W. Yuen, we generalize the blowup results with constant compact radius R of solutions to the case with general compact radius R(t) and to the case with no compact support restriction.