Abstract

We consider in this work the generalized relativistic Boltzmann equation in the presence of a Yang-Mills field in temporal gauge on a Bianchi type 1 space-time. Such an equation governs the evolution which collisions of plasmas, for instance of quarks and gluons (quagma), where non abelian Yang-Mills field replace the usual electromagnetic field. A local in time existence and uniqueness result for the regular solution is established, using a suitable combination of Faedo Galerkin method and fixed point theorem.