GLOBAL-IN-TIME EXISTENCE OF WEAK SOLUTIONS FOR VLASOV-MANEV-FOKKER-PLANCK SYSTEM

Abstract

We consider the Vlasov-Manev-Fokker-Planck (VMFP) system in three dimensions, which differs from the Vlasov-Poisson-Fokker-Planck in that it has the gravitational potential of the form (Formula Presented) instead of the Newtonian one. For the VMFP system, we establish the global-in-time existence of weak solutions under smallness assumption on either the initial mass or the coefficient of the pure Manev potential. The proof extends to several related kinetic systems.