Improved blowup theorems for the Euler-Poisson equations with attractive forces

Abstract

Our discussion here mainly focuses on the formation of singularities for solutions to the N-dimensional Euler-Poisson equations with attractive forces, in radial symmetry. Motivated by the integration method of Yuen, we prove two blow-up results under the conditions that the solutions have compact radius R(t) or have no compact support restriction, which generalize the ones Yuen obtained in 2011 [M. W. Yuen, “Blowup for the C1 solution of the Euler-Poisson equations of gaseous stars in RN,” J. Math. Anal. Appl. 383, 627-633 (2011)].