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arXiv · 1201.6048

Regularity of solutions of the fractional porous medium flow

Luis Caffarelli·Fernando Soria·Juan Luis Vazquez
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Abstract

We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. More precisely, $$ u_t=\nabla\cdot(u\nabla (-Δ)^{-s}u), \quad \ 0<s<1. $$ The problem is posed in $\{x\in\ren, t\in \re\}$ with nonnegative initial data $u(x,0)$ that are integrable and decay at infinity. A previous paper has established the existence of mass-preserving, nonnegative weak solutions satisfying energy estimates and finite propagation. Here we establish the boundedness and $C^α$ regularity of such weak solutions

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Luis Caffarelli, Fernando Soria, Juan Luis Vazquez. 2012-01-29. Regularity of solutions of the fractional porous medium flow. https://arxiv.org/abs/1201.6048

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