Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets
We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized proble...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/595819 |
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| author | Davide Catania |
| author_facet | Davide Catania |
| author_sort | Davide Catania |
| collection | DOAJ |
| description | We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives. This is a preliminary result to the study of linearized variable-coefficient current-vortex sheets, a first step to prove the existence of solutions to the nonlinear problem. |
| format | Article |
| id | doaj-art-b1ac768842bb43138cadce7ab68fe438 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b1ac768842bb43138cadce7ab68fe4382025-02-03T07:25:45ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/595819595819Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex SheetsDavide Catania0Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, ItalyWe consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives. This is a preliminary result to the study of linearized variable-coefficient current-vortex sheets, a first step to prove the existence of solutions to the nonlinear problem.http://dx.doi.org/10.1155/2013/595819 |
| spellingShingle | Davide Catania Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets International Journal of Differential Equations |
| title | Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets |
| title_full | Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets |
| title_fullStr | Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets |
| title_full_unstemmed | Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets |
| title_short | Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets |
| title_sort | existence and stability for the 3d linearized constant coefficient incompressible current vortex sheets |
| url | http://dx.doi.org/10.1155/2013/595819 |
| work_keys_str_mv | AT davidecatania existenceandstabilityforthe3dlinearizedconstantcoefficientincompressiblecurrentvortexsheets |