We consider a family of porous media equations with fractional pressure, 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.
A gradient flow approach to the porous medium equation with fractional pressure
LISINI, STEFANO;SEGATTI, ANTONIO GIOVANNI
2018-01-01
Abstract
We consider a family of porous media equations with fractional pressure, 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.File in questo prodotto:
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