Abstract
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.
Highlights
We study the coupled Maxwell-BoltzmannEuler system which governs the collisional evolution of a kind of fast moving, massive, and charged particles and which is one of the basic systems of the kinetic theory
The physical significance of the work we did in the present paper is the study of the global dynamics of a kind of fast moving, massive, and charged particles, in the case where the gravitational forces are neglected in front of the electromagnetic forces
We have coupled the Maxwell-Boltzmann system with the Euler equations which express the conservation of the Stress-matter tensor for the unknown Φ representing a massive scalar field
Summary
We study the coupled Maxwell-BoltzmannEuler system which governs the collisional evolution of a kind of fast moving, massive, and charged particles and which is one of the basic systems of the kinetic theory.The spacetimes considered here are the Bianchi of types I to VIII spacetimes where homogeneous phenomena such as the one we consider here are relevant. Note that the whole universe is modeled and particles in the kinetic theory may be particles of ionized gas as nebular galaxies or even cluster of galaxies, burning reactors, and solar wind, for which only the evolution in time is really significant, showing thereafter the importance of homogeneous phenomena. The relativistic Boltzmann equation rules the dynamics of a kind of particles subject to mutual collisions, by determining their distribution function, which is a nonnegative real-valued function of both the position and the momentum of the particles. This function is interpreted as the probability of the presence density of the particles in a given volume, during their collisional evolution. The operator acts only on the momentum of the particles and describes, at any time, at each point where two particles collide with each other, the effects of the behaviour imposed by the collision on the distribution function, taking in account the fact that the momentum of each particle is not the same, before and after the collision, with only the sum of their two momenta being preserved
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