A gradient flow approach to the porous medium equation with fractional   pressure
  We consider a family of fractional porous media equations, recently studied by Caffarelli and V\'azquez. 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. 
Stefano Lisini, Edoardo Mainini and Antonio Segatti
math.AP