Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces - Ahmed El Idrissi; Halima Srhiri; Brahim Boukari; Jalila El Ghordaf (Electronic Journal of Differential Equations)
In this article we study fractional porous medium equations in Besov-Morrey spaces. Using the Littlewood-Paley theory and the smoothing effect of the heat semi-group, we obtain local well-posedness of this model. Also, we obtain global well-posedness for small initial data in the critical Besov-Morrey spaces $ \dot{\mathcal{N}}_{p,h,∞}^{-2m+\frac{n}{p}}(\mathbb{R}^n)$ with $1/2<m< 1$, $\max\{ 1,\frac{n}{2m}\} <p<∞$ and $1≤ h≤ p$.