The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

This work proves the global stability of the Boltzmann equation (1872) with the physical
collision kernels derived by Maxwell in 1866 for the full range of inverse-power …

We study Boltzmann's collision operator for long-range interactions, ie, without Grad's
angular cut-off assumption. We establish a functional inequality showing that the entropy …

We review recent results about Boltzmann equation for singular or non cutoff cross-sections.
Both spatially homogeneous and inhomogeneous Boltzmann equations are considered …

We study the Boltzmann equation without Grad's angular cutoff assumption. We introduce a
suitable renormalized formulation that allows the cross section to be singular in both the …

Abstract The Boltzmann equation without Grad's angular cutoff assumption is believed to
have a regularizing effect on the solutions because of the non-integrable angular singularity …

We prove the global existence and uniqueness of classical solutions around an equilibrium
to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the …

In this paper we prove new constructive coercivity estimates for the Boltzmann collision
operator without cutoff, that is for long-range interactions. In particular we give a generalized …

We apply recent results on regularity for general integro-differential equations to derive a
priori estimates in Hölder spaces for the space homogeneous Boltzmann equation in the …

This article provides sharp constructive upper and lower bound estimates for the Boltzmann
collision operator with the full range of physical non-cut-off collision kernels (γ>− n and …