21 research outputs found
GLOBAL REGULAR SOLUTION FOR THE EINSTEIN-MAXWELL-BOLTZMANN-SCALAR FIELD SYSTEM IN A BIANCHI TYPE-I SPACE-TIME
We prove an existence and uniqueness of regular solution to the Einstein-Maxwell-Boltzmann-Scalar Field system with pseudo-tensor of pressure and the cosmological constant globaly in time. We clarify the choice of the function spaces and we establish step by step all the essential energy estimations leading to the global existence theorem
Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
We prove in the cases of spherical, plane and hyperbolic symmetry a local in
time existence theorem and continuation criteria for cosmological solutions of
the Einstein-Vlasov-scalar field system, with the sources generated by a
distribution function and a scalar field, subject to the Vlasov and wave
equations respectively. This system describes the evolution of self-gravitating
collisionless matter and scalar waves within the context of general relativity.
In the case where the only source is a scalar field it is shown that a global
existence result can be deduced from the general theorem.Comment: 33 pages, typos corrected, second conclusion of theorem 4.5 and
remark 4.6 remove
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
Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi type I space-time
We prove, for the relativistic Boltzmann equation on a Bianchi type I
space-time, a global existence and uniqueness theorem, for arbitrarily large
initial data.Comment: 17 page