Global Regular Solution for the Einstein-Maxwell-Boltzmann-Scalar Field System in a Bianchi Type-I Space-Time

Norbert, Noutchegueme

doi:10.24297/jam.v13i1.5982

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“…In the abelian case, forces created by charged particles are electromagnetic forces and when we consider particles evolving with collisions, the self-mained phenomenon is governed by the Maxwell-Boltzmann system. Many authors have studied the Boltzmann equation alone or coupled with other type of equations for instance, we can refer to [4,13,14,15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Regular Solution for the Generalized Relativistic Boltzmann Equation in Yang-Mills Field

Dongo¹,

Noutchegueme²,

Abel³

2019

(GLM)

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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.

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