Blowup solutions for a class of fluid dynamical equations in [formula omitted

Abstract

In this paper, we consider the blowup solutions for the Euler–Poisson type equations, such as isentropic Euler–Poisson, Navier–Stokes–Poisson, Euler and Navier–Stokes equations, and the systems with frictional damping. It is shown that these systems have similar blowup phenomenon which generalize the previous results of the blowup solution for the Euler–Poisson equations for gaseous stars. Besides the blowup rate is given. Furthermore, under the assumption ρ r = 0 , some radial symmetric blowup solutions for the Euler–Poisson type equations are given.