arXiv subjects

Norbert Noutchegueme

Publications and source records attributed to Norbert Noutchegueme.

10 recordsLinked to original sources

arXiv2019

Global Dynamics for a relativistic charged and colliding plasma in presence of a massive scalar field on the Robertson-Walker spacetime

We consider the coupled Einstein-Maxwell-Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman-Lemaître-Robertson-Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables $(x^i)$, $i=1,2,3$. By combining the energy estimates method with that of characteristics we derive under suitable conditions on the chock kernel (see Eq. 2.20), a local (in time) solution of the coupled system. Further, under the hypotheses that the data are small in some appropriate norms and that the cosmological constant satisfies $Λ> -4πm^2Φ_0^2$, we derive a unique global (in time) solution (Theorem 6.1).

math.AP↗

arXiv2015

Global Dynamics for the coupled Einstein-Maxwell system with pseudo-tensor of pressure on Bianchi spacetimes

Global existence to the coupled Einstein-Maxwell system which rules the dynamics of a kind of charged matter with a pseudo-tensor of pressure is proved, in Bianchi I-VIII spacetimes. We study the geodesics completeness, the asymptotic behavior, the positivity conditions, and we prove that the problem is well-posed in the sense of Hadamard.

gr-qc↗

arXiv2012

Einstein-Maxwell-Massive Scalar Field System in 3+1 formulation on Bianchi Spacetimes type I-VIII

Global existence to the coupled Einstein-Maxwell-Massive Scalar Field system which rules the dynamics of a kind of charged pure matter in the presence of a massive scalar field is proved, in Bianchi I-VIII spacetimes; asymptotic behaviour, geodesic completeness, energy conditions are investigated in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the massive scalar field.

gr-qc↗

arXiv2006

Global existence of solutions for the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time for arbitrarily large initial data

We prove a global in time existence theorem for the initial value problem for the Einstein-Boltzmann system, with positive cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.

gr-qc↗

arXiv2006

Global existence of solutions for the relativistic Boltzmann equation on the flat Robertson-Walker space-time for arbitrarily large intial data

We prove a global result in time for the initial value problem for the relativistic Boltzmann equation on the flat Robertson-Walker sapace time, in the functional framework appropriate to the coupling with Einstein's equations. We had nowhere to restrict the size of the initial data which can hence be taken arbitrarily large.

gr-qc↗

arXiv2005

Global Existence of Solutions for the Einstein-Boltzmann System in a Bianchi Type I Space-Time

We prove a global in time existence theorem, for the initial value problem for the Einstein-Boltzmann system, with arbitrarily large initial data, in the homogeneous case, in a Bianchi type I space-time

gr-qc↗

arXiv2005

Global Existence of Solutions for the Einstein-Boltzmann System with Cosmological Constant in the Robertson-Walker Space-time

We prove a global in time existence theorem for the initial values problem for the Einstein-Boltzmann system with cosmological constant and arbitrarily large initial data, in the spatially homogeneous case, in a Robertson-Walker space-time.

gr-qc↗

arXiv2004

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.

gr-qc↗

arXiv2003

The surface-symmetric Einstein-Vlasov system with cosmological constant

The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological constant there is a large class of initial data with global existence and inflationary asymptotics in the future as in the case of plane or hyperbolic symmetry treated in [7]. Furthermore we analyze the behaviour of the energy-momentum tensor at late times.

gr-qc↗

arXiv2003

Global solutions for the relativistic Boltzmann equation in the homogeneous case on the Minkowski space-time

We prove, for the relativistic Boltzmann equation in the homogeneous case, on the Minkowski space-time, a global in time existence and uniqueness theorem. The method we develop extends to the cases of some curved space-times such as the flat Robertson-Walker space-time and some Bianchi type I space-times.

gr-qc↗