The Maxwell-Boltzmann-Euler System with a Massive Scalar Field in All Bianchi Spacetimes

We prove the existence and uniqueness of regular solution to the coupled Maxwell-Boltzmann-Euler system, which governs the collisional evolution of a kind of fast moving, massive, and charged particles, globally in time, in a Bianchi of types I to VIII spacetimes. We clearly define function spaces, and we establish all the essential energy inequalities leading to the global existence theorem

Dynamical Methods for Global Solutions to a Minimally Coupled Massive Scalar Field Theory in Bianchi Type I Anisotropic Model: Hamiltonian Formalism, Singularities and Isotropization of Universe

Abstract Using the ADM formalism, we establish and solve globally in time, Hamilton's equations by the means of a dynamical analysis, for a Bianchi type I model. Singularities and isotropization of the Universe both at early and late times are also investigated. Mathematics Subject Classifications: 83Cx