Inserted: 25 jun 2016
Last Updated: 27 oct 2017
Journal: Arch. Ration. Mech. Anal.
We consider a family of fractional porous media equations, recently studied by Caffarelli and Vazquez. We show the construction of a weak solution as Wasserstein gradient flow of a square fractional Sobolev norm. Energy dissipation inequality, regularizing effect and decay estimates for the $L^p$ norms are established. Moreover, we show that a classical porous medium equation can be obtained as a limit case.