Abstract
This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.
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