Classical Solution for the Boltzmann Equation with Absorption Term in Yang-Mills Field - Dongo, David; Noutchegueme, Norbert; Nguelemo, Abel Kenfack (Communications in Mathematics and Applications, 2020)
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.
Keywords: Boltzmann equation; Absorption term; Yang-Mills field; Classical solution; Bianchi type 1