Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 80, pp. 1-16.

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

Authors: Ahmed El Idrissi (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)
         Halima Srhiri (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)
         Brahim El Boukari (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)
         Jalila El Ghordaf (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)

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 $1\leq h\leq p$.

Submitted April 13, 2025. Published August 04, 2025.
Math Subject Classifications: 35K55, 35K15, 30H25.
Key Words: Nonlinear diffusion; fractional porous medium equation; local and global 
    well-posedness; Besov-Morrey spaces; fractional Laplacians.