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-M...
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| Format: | Article |
| Language: | English |
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Texas State University
2025-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/80/abstr.html |
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| author | Ahmed El Idrissi Halima Srhiri Brahim Boukari Jalila El Ghordaf |
| author_facet | Ahmed El Idrissi Halima Srhiri Brahim Boukari Jalila El Ghordaf |
| author_sort | Ahmed El Idrissi |
| collection | DOAJ |
| description | 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 $1\leq h\leq p$. |
| format | Article |
| id | doaj-art-e27b2f89962a4e5cb4fde2de59a1ea31 |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-e27b2f89962a4e5cb4fde2de59a1ea312025-08-20T03:46:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-08-01202580,116Local and global solvability of fractional porous medium equations in critical Besov-Morrey spacesAhmed El Idrissi0Halima Srhiri1Brahim Boukari2Jalila El Ghordaf3 Sultan Moulay Slimane Univ., Beni Mellal, Morocco Sultan Moulay Slimane Univ., Beni Mellal, Morocco Sultan Moulay Slimane Univ., Beni Mellal, Morocco Sultan Moulay Slimane Univ., Beni Mellal, Morocco 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 $1\leq h\leq p$.http://ejde.math.txstate.edu/Volumes/2025/80/abstr.htmlnonlinear diffusionfractional porous medium equationlocal and global well-posednessbesov-morrey spacesfractional laplacians |
| spellingShingle | Ahmed El Idrissi Halima Srhiri Brahim Boukari Jalila El Ghordaf Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces Electronic Journal of Differential Equations nonlinear diffusion fractional porous medium equation local and global well-posedness besov-morrey spaces fractional laplacians |
| title | Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces |
| title_full | Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces |
| title_fullStr | Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces |
| title_full_unstemmed | Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces |
| title_short | Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces |
| title_sort | local and global solvability of fractional porous medium equations in critical besov morrey spaces |
| topic | nonlinear diffusion fractional porous medium equation local and global well-posedness besov-morrey spaces fractional laplacians |
| url | http://ejde.math.txstate.edu/Volumes/2025/80/abstr.html |
| work_keys_str_mv | AT ahmedelidrissi localandglobalsolvabilityoffractionalporousmediumequationsincriticalbesovmorreyspaces AT halimasrhiri localandglobalsolvabilityoffractionalporousmediumequationsincriticalbesovmorreyspaces AT brahimboukari localandglobalsolvabilityoffractionalporousmediumequationsincriticalbesovmorreyspaces AT jalilaelghordaf localandglobalsolvabilityoffractionalporousmediumequationsincriticalbesovmorreyspaces |