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arXiv · 1606.06787

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

Stefano Lisini·Edoardo Mainini·Antonio Segatti
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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.

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Stefano Lisini, Edoardo Mainini, Antonio Segatti. 2017-10-10. A gradient flow approach to the porous medium equation with fractional pressure. https://doi.org/10.1007/s00205-017-1168-2

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