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 …

We consider a parabolic equation in nondivergence form, defined in the full space [0,∞)× R
d, with a power nonlinearity as the right-hand side. We obtain an upper bound for the …

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

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

Motivated by the question of existence of global solutions, we obtain pointwise upper
bounds for radially symmetric and monotone solutions to the homogeneous Landau …

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 consider the spatially inhomogeneous Landau equation with soft potentials. First, we
establish the short-time existence of solutions, assuming the initial data has sufficient decay …