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 …

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 consider the homogeneous and inhomogeneous Landau equation for very soft and
Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not …

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 …

In this article, we show local-in-time existence of strong solutions to the homogeneous
Landau equation with Coulomb potential for general initial datum $ f_ {in}\in L^ p $ for $ p …

We consider the Cauchy problem for the spatially inhomogeneous Landau equation with
soft potentials in the case of large (ie non-perturbative) initial data. We construct a solution …

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 …