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 …

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in
statistical mechanics. From the mathematical point of view, the existence of global smooth …

The Boltzmann equation without the angular cutoff is considered when the initial data is a
small perturbation of a global Maxwellian and decays algebraically in the velocity variable …

We survey some new results regarding a priori regularity estimates for the Boltzmann and
Landau equations conditional to the boundedness of the associated macroscopic quantities …

For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the
spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with …

The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study
wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system …

We present some essential properties of solutions to the homogeneous Landau-Fermi-Dirac
equation for moderately soft potentials. Uniform in time estimates for statistical moments, L p …

We study the spatially inhomogeneous Landau equations with hard potential in the
perturbation setting, and establish the analytic smoothing effect in both spatial and velocity …

The known nonlinear kinetic equations (in particular, the wave kinetic equation and the
quantum Nordheim--Uehling--Uhlenbeck equations) are considered as a natural …

The Boltzmann equation is studied without the cutoff assumption. Under a perturbative
setting, a unique global solution of the Cauchy problem of the equation is established in a …