* C. Buet, S. Cordier *

**Résumé:** Homogeneous Fokker-Planck-Landau equation is investigated for
coulombian potential and isotropic distribution function i.e. when the distribution function depends only on time and on the modulus of the velocity. We derive a new conservative and entropy decaying semi-discretized Landau equation for which we prove the
existence of global in time positive solutions. For the time-discretized equation, we give lower bound for the time step which guaranteed positivity and entropy decaying of the numerical solution.

**Mots Clés:** *Kinetic models, Fokker-Planck-Landau equation, System of ordinary differential equations, Cauchy problem *