Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.