Global Solutions and Stability for Self-Gravitating Isentropic Gases

The global solution to the radial motion of self-gravitating gases is studied. The global approximate solutions are constructed by a generalized shock capturing method. The nonlocal terms are carefully estimated. The uniform estimate of the approximate solutions is obtained. The convergence of the approximate solutions is proved by the compensated compactness method. The global existence of weak entropy solution with arbitrarily large L` initial data is then established