Cercignani's conjecture assumes a linear inequality between the entropy and entropy
production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics …

The aim of the present paper is twofold: 1. We carry on with developing an abstract method
for deriving decay estimates on the semigroup associated to non-symmetric operators in …

This work deals with the Landau equation for very soft and Coulomb potentials near the
associated Maxwellian equilibrium. We first investigate the corresponding linearized …

When dilute charged particles are confined in a bounded domain, boundary effects are
crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov …

This paper gives an affirmative answer to the question of the global existence of Boltzmann
equations without angular cutoff in the L∞-setting. In particular, we show that when the initial …

Hypocoercivity methods are applied to linear kinetic equations with mass conservation and
without confinement in order to prove that the solutions have an algebraic decay rate in the …

This work deals with the inhomogeneous Landau equation on the torus in the cases of hard,
Maxwellian and moderately soft potentials. We first investigate the linearized equation and …

The global well-posedness of the Boltzmann equation with initial data of large amplitude has
remained a long-standing open problem. In this paper, by developing a new L^\infty_xL^ 1 …

In a general C 1 domain, we study the perturbative Cauchy theory for the Boltzmann
equation with Maxwell boundary conditions with an accommodation coefficient α in (2/3, 1] …

In this paper, we investigate the problems of Cauchy theory and exponential stability for the
inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical …