On the ill posedness of force-free electrodynamics in Euler potentials

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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Bibliographic Details
Main Authors: Reula, Oscar Alejandro, Rubio, Marcelo Enrique
Other Authors: https://orcid.org/0000-0003-2517-7454
Format: info:eu-repo/semantics/submittedVersion biblioteca
Language:eng
Published: 2017
Subjects:Force-free electrodynamics, Euler potentials, Well posedness, Strong hyperbolicity,
Online Access:http://hdl.handle.net/11086/553295
https://doi.org/10.48550/arXiv.1611.06415
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spelling dig-unc-ar-11086-5532952024-08-16T06:38:34Z 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
institution UNC AR
collection DSpace
country Argentina
countrycode AR
component Bibliográfico
access En linea
databasecode dig-unc-ar
tag biblioteca
region America del Sur
libraryname Biblioteca 'Ing. Agrónomo Moisés Farber' de la Facultad de Ciencias Agropecuarias
language eng
topic Force-free electrodynamics
Euler potentials
Well posedness
Strong hyperbolicity
Force-free electrodynamics
Euler potentials
Well posedness
Strong hyperbolicity
spellingShingle Force-free electrodynamics
Euler potentials
Well posedness
Strong hyperbolicity
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
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
author2 https://orcid.org/0000-0003-2517-7454
author_facet https://orcid.org/0000-0003-2517-7454
Reula, Oscar Alejandro
Rubio, Marcelo Enrique
format info:eu-repo/semantics/submittedVersion
topic_facet Force-free electrodynamics
Euler potentials
Well posedness
Strong hyperbolicity
author Reula, Oscar Alejandro
Rubio, Marcelo Enrique
author_sort Reula, Oscar Alejandro
title 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_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_sort on the ill posedness of force-free electrodynamics in euler potentials
publishDate 2017
url http://hdl.handle.net/11086/553295
https://doi.org/10.48550/arXiv.1611.06415
work_keys_str_mv AT reulaoscaralejandro ontheillposednessofforcefreeelectrodynamicsineulerpotentials
AT rubiomarceloenrique ontheillposednessofforcefreeelectrodynamicsineulerpotentials
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