Global weak entropy solutions to the Euler–Poisson system with spherical symmetry

Abstract

In this paper, we study the initial boundary value problem for the isentropic Euler–Poisson system in an exterior domain with spherical symmetry. The initial data is supposed to be bounded and satisfy other suitable assumptions. Using a fractional step Godunov scheme, we construct the approximate solutions and prove the uniform [Formula: see text] estimates for the approximate solutions. Then the compensated compactness argument implies the convergence of the solutions. The weak entropy solution also satisfies the initial value and boundary value in the sense of trace.