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 paper deals with the spatially homogeneous Boltzmann equation when grazing
collisions are involved. We study in a unified setting the Boltzmann equation without cut-off …

The idea for this book was conceived by the authors some time in 1988, and a first outline of
the manuscript was drawn up during a summer school on mathematical physics held in …

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 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 …

On asymptotics of the Boltzmann equation when the collisions become grazing Page 1
TRANSPORT THEORY AND STATISTICAL PHYSICS, 21(3), 259-276 (1992) ON ASYMPTOTICS …

The development of accurate and fast numerical schemes for the five-fold Boltzmann
collision integral represents a challenging problem in scientific computing. For a particular …

This paper studies the approximation of the Boltzmann equation by the Landau equation in
a regime when grazing collisions prevail. While all previous results in the subject were …

We present here various compactness properties enjoyed by global solutions of the so-
called Boltzmann and Landau equations. These properties, which are crucial for the …

We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators,
for a general class of interactions including any inverse-power law interactions, and hard …