On radially symmetric solutions of the compressible isentropic self-gravitating fluid

In this paper, we mainly prove the global existence of weak solutions to the Cauchy problem for the Navier–Stokes system of compressible isentropic self-gravitating fluids in R3R3 when the Cauchy data are radially symmetric. It extends Feireisl’s existence theorem, Ducomet et al. (2001) [16], to the case 4/3<γ≤3/24/3<γ≤3/2 for radially symmetric initial data, where γγ is the specific heat ratio in the pressure. If the total mass is less than a certain critical mass, this conclusion also holds for γ=4/3γ=4/3. Furthermore, for the case of annular domain, we point out the global existence radially symmetric strong solutions when the radially symmetric initial data satisfy the compatibility condition and the initial density need not be positive.