Related papers: The spatially homogeneous relativistic Boltzmann e…

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…

We prove a local-in-time existence and uniqueness theorem for a smooth classical solution to the spatially homogeneous Boltzmann equation with cutoff soft potentials. Our proof is based on a series of bilinear estimates for the…

In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is…

We investigate the large time behavior of solutions to the spatially homogeneous linear Boltzmann equation from a semigroup viewpoint. Our analysis is performed in some (weighted) $L^{1}$-spaces. We deal with both the cases of hard and soft…

We study the spatially homogeneous relativistic Boltzmann equation for massless particles in an FLRW background with scattering kernels in a certain range of soft and hard potentials. We obtain the future global existence of small solutions…

In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to…

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…

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.

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…

In this paper we study the Boltzmann equation near global Maxwellians in the $d$-dimensional whole space. A unique global-in-time mild solution to the Cauchy problem of the equation is established in a Chemin-Lerner type space with respect…

This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off and non mollified) hard potentials. We prove an exponential in time…

We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and…

The unique global strong solution in the Chemin-Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in perturbation framework. Such solution space is of critical regularity with respect to…

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…

Departing from the weak solution, we prove the uniqueness, smoothing estimates and the global dynamics for the non cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. Our results show that the behavior of the…

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out…

In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our…

We study the Cauchy problem for the relativistic Boltzmann equation near relativistic Maxwellians in the whole space. The purpose of this article is to handle hard potentials, and for initial data with finite $L^\infty$ norm, to construct…

We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity…

We prove the existence and uniqueness of global solutions to the Boltzmann equation with non-cutoff soft potentials in the whole space when the initial data is a small perturbation of a Maxwellian with polynomial decay in velocity. Our…