Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces

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 \( Ṅp,h,∞-2m+n/p(R^n)\) with \(1/2< m< 1$, $max\{ 1,n/2m\} < p<∞\) and \(1≤ h≤ p\). For more information see https://ejde.math.txstate.edu/Volumes/2025/80/abstr.html