Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system

TL;DR

This paper proves the global-in-time existence of weak solutions for the three-dimensional Vlasov-Manev-Fokker-Planck system with a specific gravitational potential, extending the analysis to related kinetic models.

Contribution

It establishes the first global-in-time existence results for weak solutions of the VMFP system with Manev potential, a significant extension of kinetic theory.

Findings

Proved global existence of weak solutions for VMFP system.

Extended the proof technique to related kinetic systems.

Demonstrated the applicability of methods to non-Newtonian potentials.

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 $-1/r - 1/r^2$ instead of the Newtonian one. For the VMFP system, we establish the global-in-time existence of weak solutions. The proof extends to several related kinetic systems.