Well-posedness for the fractional Fokker-Planck equations

Abstract

In this paper, we study the fractional Fokker-Planck equation and obtain the existence and uniqueness of weak Lp-solutions (1 ⩽ p ⩽ ∞) under the assumptions that the coefficients are only in Sobolev spaces. Moreover, to L∞-solutions, we gain the well-posedness for BV coefficients. Besides, the non-negative weak Lp-solutions and renormalized solutions are derived. After then, we achieve the stability for stationary solutions.