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 \begin{document}$ -1/r - 1/r^2 $\end{document} 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.