VISCOSITY SOLUTIONS FOR THE INHOMOGENEOUS RELATIVISTIC VLASOV EQUATION ON A SPHERICALLY SYMMETRIC GRAVITATIONAL FIELD SPACE-TIME

The viscosity solution for the inhomogeneous relativistic Vlasov equation is investigated. We consider this equation on a spherically symmetric gravitational field space-time. We rigorously prove the existence result of the viscosity solution using method of vanishing viscosity and uniqueness result of this type of solution using comparison method in details.