We develop a new method for proving hypocoercivity for a large class of linear kinetic
equations with only one conservation law. Local mass conservation is assumed at the level …

As part of our study of convergence to equilibrium for spatially inhomogeneous kinetic
equations, started in [21], we derive estimates on the rate of convergence to equilibrium for …

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 …

Perhaps the most fundamental model for dynamics of dilute charged particles is described
by the Vlasov-Maxwell-Boltzmann system, in which particles interact with themselves …

We consider both soft potentials with angular cutoff and Landau collision kernels in the
Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given …

This paper proves the existence of small‐amplitude global‐in‐time unique mild solutions to
both the Landau equation including the Coulomb potential and the Boltzmann equation …

For a general class of linear collisional kinetic models in the torus, including in particular the
linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard …

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

It is known that the singularity in the non-cutoff cross-section of the Boltzmann equation
leads to the gain of regularity and a possible gain of weight in the velocity variable. By …

Given a normalized Maxwellian μ and n≥ 1, we establish the global‐in‐time validity of a
diffusive expansion (0.1)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, F^ ε (t, x, v)=\mu+ μ\left {ε f_ 1 (t, x, v)+ ε^ 2 f_ 2 (t, x …