Nonlinear Fokker-Planck equations with singular integral drifts and McKean-Vlasov SDEs

TL;DR

This paper establishes the well-posedness of nonlinear Fokker-Planck equations with singular drifts in Sobolev spaces and applies these results to demonstrate the existence of strong solutions for McKean-Vlasov equations.

Contribution

It introduces a novel approach to handle singular drifts in nonlinear Fokker-Planck equations and applies this to prove strong solutions for McKean-Vlasov SDEs.

Findings

Well-posedness in H^{-1} for nonlinear Fokker-Planck equations with singular drifts

Existence of strong solutions for McKean-Vlasov equations

Extension of analytical techniques to singular drift scenarios

Abstract

One proves the well-posedness in the Sobolev space H^{-1} of nonlinear Fokker-Planck equations with singular drifts.Applications to existence of strong solutions to McKean-Vlasov equations are given.