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

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, $\alpha>\frac d2+1$. Besides, we correct a mistake in our previous paper \cite{zhou01}.