Numerical Analysis of the Isotropic Fokker–Planck–Landau Equation

The homogeneous Fokker–Planck–Landau equation is investigated for Coulombic potential and isotropic distribution function, i.e., when the distribution function de- pends only on time and on the modulus of the velocity. We derive a conservative and entropy decaying semidiscretized Landau equation for which we prove the exis- tence of global in-time positive solutions. This scheme is not based on the so-called “Landau–Log” formulation of the operator and ensures the physically relevant long- time behavior of the solution