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 …

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 …

In this article we consider direct and inverse problems for α-stable, elliptic nonlocal
operators whose kernels are possibly only supported on cones and which satisfy the …

In the paper, for the Cauchy problem on the non-cutoff Boltzmann equation in torus, we
establish the global-in-time Gevrey smoothness in velocity and space variables for a class of …

In this article we study the Gevrey regularization effect for the spatially inhomogeneous
Boltzmann equation without angular cutoff. This equation is partially elliptic in the velocity …

Motivated by the open problem of large-data global existence for the non-cutoff Boltzmann
equation, we introduce a model equation that in some sense disregards the anisotropy of …

In this paper we study the regularity of the non-cutoff Vlasov–Poisson–Boltzmann system for
plasma particles of two species in the whole space R^ 3 R 3 with hard potential. The …

We propose an entropic Fourier method for the numerical discretization of the Boltzmann
collision operator. The method, which is obtained by modifying a Fourier--Galerkin method …

We consider the Cauchy problem of the nonlinear Landau equation of Maxwellian
molecules, under the perturbation frame work to global equilibrium. We show that if $ H^ r_x …

Abstract We study the Vlasov–Poisson–Boltzmann system without angular cutoff and the
Vlasov–Poisson–Landau system with all hard potentials in the perturbation setting, and …