Well-posedness for the fractional Fokker-Planck equations

In this paper, we study the fractional Fokker-Planck equation and obtain the existence and uniqueness of weak L-p-solutions (1 <= p <= infinity) under the assumptions that the coefficients are only in Sobolev spaces. Moreover, to L-infinity-solutions, we gain the well-posedness for BV coefficients. Besides, the non-negative weak L-p-solutions and renormalized solutions are derived. After then, we achieve the stability for stationary solutions. (C) 2015 AIP Publishing LLC.