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

Abstract

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 \( \dot{\mathcal{N}}_{p,h,\infty}^{-2m+\frac{n}{p}}(\mathbb{R}^n)\) with \(1/2< m< 1$, $\max\{ 1,\frac{n}{2m}\} < p<\infty\) and \(1\leq h\leq p\). For more information see https://ejde.math.txstate.edu/Volumes/2025/80/abstr.html