Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces

Weiliang Xiao, Xuhuan Zhou

Published 2016-03-06Version 1

We study the well-posedness of the fractional porous medium flow with nonlocal diffusion effects. The model is based on Darcy's law and the pressure is given by an inverse fractional Laplacian operator. We prove the local well-posedness result of the equation in the Sobolev spaces $H^\alpha$ with nonnegative initial data in $H^\alpha$, for $\alpha>\frac d2+1$.