On the ill posedness of force-free electrodynamics in Euler potentials
Artículo finalmente publicado en: Reula, O. A. y Rubio, M. E. (2017). Ill posedness of force-free electrodynamics in Euler potentials. Physical Review D, 95 (6), 064005. https://doi.org/10.1103/PhysRevD.95.064005
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| Format: | info:eu-repo/semantics/submittedVersion |
| Language: | eng |
| Published: |
2024
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| Online Access: | http://hdl.handle.net/11086/553295 https://doi.org/10.48550/arXiv.1611.06415 |
| _version_ | 1808112608483475456 |
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| author | Reula, Oscar Alejandro Rubio, Marcelo Enrique |
| author2 | https://orcid.org/0000-0003-2517-7454 |
| author_facet | https://orcid.org/0000-0003-2517-7454 Reula, Oscar Alejandro Rubio, Marcelo Enrique |
| author_sort | Reula, Oscar Alejandro |
| collection | Repositorio Digital Universitario |
| description | Artículo finalmente publicado en: Reula, O. A. y Rubio, M. E. (2017). Ill posedness of force-free electrodynamics in Euler potentials. Physical Review D, 95 (6), 064005. https://doi.org/10.1103/PhysRevD.95.064005 |
| format | info:eu-repo/semantics/submittedVersion |
| id | rdu-unc.553295 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2024 |
| record_format | dspace |
| spelling | rdu-unc.5532952024-08-16T06:38:34Z On the ill posedness of force-free electrodynamics in Euler potentials Reula, Oscar Alejandro Rubio, Marcelo Enrique https://orcid.org/0000-0003-2517-7454 https://orcid.org/0000-0002-7298-3128 Force-free electrodynamics Euler potentials Well posedness Strong hyperbolicity Artículo finalmente publicado en: Reula, O. A. y Rubio, M. E. (2017). Ill posedness of force-free electrodynamics in Euler potentials. Physical Review D, 95 (6), 064005. https://doi.org/10.1103/PhysRevD.95.064005 info:eu-repo/semantics/submittedVersion Fil: Reula, Oscar Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Reula, Oscar Alejandro. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina. Fil: Rubio, Marcelo Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Rubio, Marcelo Enrique. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Fil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina. We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed. We establish this result by showing that a well-posedness criterion provided by Kreiss fails to hold for this theory, and using a theorem provided by Strang. To show the nature of the problem we display a particular bounded (in Sobolev norms) sequence of initial data for the Force-free equations such that at any given time as close to zero as one wishes, the corresponding evolution sequence is not bounded. Thus, the Force-free evolution is non continuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.064005 info:eu-repo/semantics/submittedVersion Fil: Reula, Oscar Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Reula, Oscar Alejandro. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina. Fil: Rubio, Marcelo Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. Fil: Rubio, Marcelo Enrique. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Fil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina. Matemática Pura 2024-08-15T13:34:25Z 2024-08-15T13:34:25Z 2017 article 2470-0010 http://hdl.handle.net/11086/553295 2470-0029 https://doi.org/10.48550/arXiv.1611.06415 eng De la versión publicada: https://doi.org/10.1103/PhysRevD.95.064005 Atribución-NoComercial-SinDerivadas 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es Impreso; Electrónico y/o Digital |
| spellingShingle | Force-free electrodynamics Euler potentials Well posedness Strong hyperbolicity Reula, Oscar Alejandro Rubio, Marcelo Enrique On the ill posedness of force-free electrodynamics in Euler potentials |
| title | On the ill posedness of force-free electrodynamics in Euler potentials |
| title_full | On the ill posedness of force-free electrodynamics in Euler potentials |
| title_fullStr | On the ill posedness of force-free electrodynamics in Euler potentials |
| title_full_unstemmed | On the ill posedness of force-free electrodynamics in Euler potentials |
| title_short | On the ill posedness of force-free electrodynamics in Euler potentials |
| title_sort | on the ill posedness of force free electrodynamics in euler potentials |
| topic | Force-free electrodynamics Euler potentials Well posedness Strong hyperbolicity |
| url | http://hdl.handle.net/11086/553295 https://doi.org/10.48550/arXiv.1611.06415 |
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