We extend the De Giorgi--Nash--Moser theory to a class of kinetic Fokker-Planck equations
and deduce new results on the Landau-Coulomb equation. More precisely, we first study the …

The existence and stability of the Landau equation (1936) in a general bounded domain
with a physical boundary condition is a long-outstanding open problem. This work proves …

This paper deals with the space-homogenous Landau equation with very soft potentials,
including the Coulomb case. This nonlinear equation is of parabolic type with diffusion …

We consider solutions to the space-homogeneous Landau equation with a general family of
interaction potentials. We prove that their Fisher information is monotone decreasing in time …

arXiv:1906.02841v1 [math.AP] 6 Jun 2019 Page 1 arXiv:1906.02841v1 [math.AP] 6 Jun 2019
PARTIAL REGULARITY IN TIME FOR THE SPACE HOMOGENEOUS LANDAU EQUATION …

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 …

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 …

We describe a time-dependent functional involving the relative entropy and the PH1
seminorm, which decreases along solutions to the spatially homogeneous Landau equation …

We consider the spatially homogeneous Landau equation with Coulomb potential. We show
short time propagation of smallness in norms for and instantaneous regularization in …

We propose a hybrid framework opPINN: physics-informed neural network (PINN) with
operator learning for approximating the solution to the Fokker-Planck-Landau (FPL) …