We propose a novel deterministic particle method to numerically approximate the Landau
equation for plasmas. Based on a new variational formulation in terms of gradient flows of …

We propose a gradient flow perspective to the spatially homogeneous Landau equation for
soft potentials. We construct a tailored metric on the space of probability measures based on …

We prove a Schauder estimate for kinetic Fokker-Planck equations that requires only H\"
older regularity in space and velocity but not in time. As an application, we deduce a weak …

We are concerned with the uniqueness of weak solution to the spatially homogeneous
Landau equation with Coulomb interactions under the assumption that the solution is …

In this paper, we introduce Prodi–Serrin like criteria which enable us to provide a priori
estimates for the solutions to the spatially homogeneous Landau equation for all classical …

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 …

The global in time existence of weak solutions to a cross-diffusion system with fractional
diffusion in the whole space is proved. The equations describe the evolution of multi-species …

In this paper, we prove global-in-time existence and uniqueness of smooth solutions to the
homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions …

Following the recent ideas of Guillen and Silvestre in $[9] $, we prove that the Fisher
information is non-increasing along the flow of the isotropic Landau equation. We then use …

We consider the equation ut= div (au∇ u− u∇ au),− Δ a= u.\displaystyle u_t= div\,(au ∇ uu
∇ au),\qquad-Δ a= u. This model has attracted some attention in the recent years and …