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A gradient flow approach to the porous medium equation with fractional pressure. (arXiv:1606.06787v2 [math.AP] UPDATED)
来源于:arXiv
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. 查看全文>>