Abstract
The Landau equation is used to describe collisions between charged particles in a plasma. It is a classic model of kinetic theory, and has been studied mathematically since the 1970s. Over the last ten years or so, it has become apparent that in the spatially homogeneous case, the structure of the equation bears many similarities to that of the 3D incompressible Navier-Stokes equation. In particular, several results have recently been obtained for the Landau equation that have a counterpart in the theory of fluid mechanics equations. In particular, we will detail a conditional regularity result of the " Prodi-Serrin " type for the Landau equation, obtained in collaboration with Ricardo Alonso, Véronique Bagland and Bertrand Lods.
