On Spherically Symmetric Motions Of a Viscous Compressible Barotropic and Selfgravitating Gas

We consider the Cauchy problem for the equations of spherically symmetric motions in \mathbb R³{\mathbb {R}^3}, of a selfgravitating barotropic gas, with possibly non monotone pressure law, in two different situations: in the first one we suppose that the viscosities μ(ρ), and λ(ρ) are density-dependent and satisfy the Bresch–Desjardins condition, in the second one we consider constant densities. In the two cases, we prove that the problem admits a global weak solution, provided that the polytropic index γ satisfy γ > 1.