Abstract

The Landau equation, introduced by Lev Landau in 1936, is a modification of the Boltzmann equation to specific applications in plasma physics, and describes the interactions and collisions among charged particles in a plasma. The mathematical investigation of the Landau equation has been active for several decades, with researchers exploring various aspects of its behavior and properties and has culminated in the recent global well-posedness result by Guillen and Silvestre for smooth initial data. In this talk I will present the first global well-posedness theory for the Landau-Coulomb with rough initial data and show that, even for non-smooth configurations, the equation has a very strong regularization effect thanks to the diffusion dominating the reaction at any time. I will also show a particular example of blow-down mechanism based on separation of scales.