Calculus of Variations and Geometric Measure Theory
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S. Lisini - E. Mainini - A. Segatti

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

created by mainini on 25 Jun 2016
modified on 27 Oct 2017


Published Paper

Inserted: 25 jun 2016
Last Updated: 27 oct 2017

Journal: Arch. Ration. Mech. Anal.
Year: 2017
Doi: 10.1007/s00205-017-1168-2

ArXiv: 1606.06787 PDF


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.

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