On the generalized porous medium equation in Fourier-Besov spaces

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu {\mathrm{\Lambda }}^{\beta }u=\mathrm{\nabla }\cdot (u\mathrm{\nabla }Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.