Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces
This article concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory as in [5,31], we obtain global well-posedness results of the GMHD equations with small initial data bel...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2017-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/65/abstr.html |
| _version_ | 1819090008761434112 |
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| author | Azzeddine El Baraka Mohamed Toumlilin |
| author_facet | Azzeddine El Baraka Mohamed Toumlilin |
| author_sort | Azzeddine El Baraka |
| collection | DOAJ |
| description | This article concerns the Cauchy problem of the 3D generalized incompressible
magneto-hydrodynamic (GMHD) equations. By using the Fourier localization
argument and the Littlewood-Paley theory as in [5,31], we
obtain global well-posedness results of the GMHD equations with small initial
data belonging to the critical Fourier-Besov-Morrey spaces.
Moreover, we prove that the corresponding global solution decays to zero
as time approaches infinity. |
| first_indexed | 2024-12-21T22:17:00Z |
| format | Article |
| id | doaj.art-21e09abab1f24d58bb881a8a2a3e0818 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T22:17:00Z |
| publishDate | 2017-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-21e09abab1f24d58bb881a8a2a3e08182022-12-21T18:48:25ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-03-01201765,120Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spacesAzzeddine El Baraka0Mohamed Toumlilin1 Univ. Mohamed Ben Abdellah, Fes, Morocco Univ. Mohamed Ben Abdellah, Fes, Morocco This article concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory as in [5,31], we obtain global well-posedness results of the GMHD equations with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover, we prove that the corresponding global solution decays to zero as time approaches infinity.http://ejde.math.txstate.edu/Volumes/2017/65/abstr.htmlMagneto-hydrodynamic equationsglobal well-posednessFourier-Besov-Morrey space |
| spellingShingle | Azzeddine El Baraka Mohamed Toumlilin Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces Electronic Journal of Differential Equations Magneto-hydrodynamic equations global well-posedness Fourier-Besov-Morrey space |
| title | Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces |
| title_full | Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces |
| title_fullStr | Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces |
| title_full_unstemmed | Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces |
| title_short | Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces |
| title_sort | global well posedness and decay results for 3d generalized magneto hydrodynamic equations in critical fourier besov morrey spaces |
| topic | Magneto-hydrodynamic equations global well-posedness Fourier-Besov-Morrey space |
| url | http://ejde.math.txstate.edu/Volumes/2017/65/abstr.html |
| work_keys_str_mv | AT azzeddineelbaraka globalwellposednessanddecayresultsfor3dgeneralizedmagnetohydrodynamicequationsincriticalfourierbesovmorreyspaces AT mohamedtoumlilin globalwellposednessanddecayresultsfor3dgeneralizedmagnetohydrodynamicequationsincriticalfourierbesovmorreyspaces |