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

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 -1=r - 1=r² 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. [ABSTRACT FROM AUTHOR]