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

Abstract

We prove the existence of a non-negative solution for a linear degenerate diffusion transport equation from which we derive the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data, $\alpha>\frac{d}{2}+1$. We also correct a mistake in our previous paper [14].

Keywords

• Fractional porous medium equation
• Sobolev space
• degenerate diffusion transport equation