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

Abstract

The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^{\alpha }$ with nonnegative initial data, $\alpha >\frac{d}{2}+1$. Besides, we correct a mistake in our previous paper \cite{zhou01}.

7 pages

References in corpus (1)

• Regularity of solutions of the fractional porous medium flow

Cited by in corpus (1)

• Mean Field Limit for Coulomb-Type Flows