Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential

International audienceWe prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (Z. Vycisl. Mat. i Mat. Fiz. 17:1063-1068, 1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked