A gradient flow approach to the porous medium equation with fractional pressure

Abstract

We consider a family of fractional porous media equations, recently studied by Caffarelli and Vázquez. 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.

34 pages

References in corpus (2)

• Nonlocal porous medium equation: Barenblatt profiles and other weak solutions
• The Fisher-KPP problem with doubly nonlinear diffusion