APDEs Seminar

We present new results on the kinetic Balescu-Lenard and Landau equations, which describe the collisional relaxation of plasma. The first result establishes global existence of solutions to the Balescu-Lenard equation for initial data close to equilibrium, while the second result shows a new blow-down mechanism for the Landau equation for a family of super-critical initial data. We also discuss the breakthrough result of Guillen and Silvestre who identify the Fisher information as a Lyapunov functional of the spatially homogeneous Landau equation. Joint work with Mitia Duerinckx and Maria Gualdani.