Classical Solution for the Boltzmann Equation with Absorption Term in Yang-Mills Field

David Dongo, Norbert Noutchegueme, Abel Kenfack Nguelemo


We consider in this work the Boltzmann equation with absorption term in the presence of an external field which is of Yang-Mills type, on a Bianchi type 1 space-time. Such an equation governs the evolution with collisions of plasmas, for instance of quarks and gluons (quagma), where non-Abelian Yang-Mills field replaces the usual electromagnetic field. A local in time existence and uniqueness result for the classical solution is established, using a suitable combination of Faedo Galerkin method and the standard iteration method. We also prove the well-posedness of the solution.


Boltzmann equation; Absorption term; Yang-Mills field; Classical solution; Bianchi type 1

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