Electron. J. Differential Equations, Vol. 2025 (2025), No. 80, pp. 1-16.
Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces
Ahmed El Idrissi, Halima Srhiri, Brahim El Boukari, Jalila El Ghordaf
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 4, 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.
DOI: 10.58997/ejde.2025.80
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Ahmed El Idrissi
LMACS Laboratory, Faculty of Science and Technology
Sultan Moulay Slimane University
Beni Mellal, 23000, Morocco
email: ahmed.elidrissi@usms.ma
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Halima Srhiri
LMACS Laboratory, Faculty of Science and Technology
Sultan Moulay Slimane University
Beni Mellal, 23000, Morocco
email: halima.srhiri.1998@gmail.com
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Brahim El Boukari
LMACS Laboratory, Faculty of Science and Technology
Sultan Moulay Slimane University
Beni Mellal, 23000, Morocco
email: elboukaribrahim@yahoo.fr
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Jalila El Ghordaf
LMACS Laboratory, Faculty of Science and Technology
Sultan Moulay Slimane University
Beni Mellal, 23000, Morocco
email: elg_jalila@yahoo.fr
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