Ill posedness of force-free electrodynamics in Euler potentials

Autores
Reula, Oscar Alejandro; Rubio, Marcelo Enrique
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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 noncontinuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Materia
FORCE-FREE
HYPERBOLIC
EULER
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/63677
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Ill posedness of force-free electrodynamics in Euler potentialsReula, Oscar AlejandroRubio, Marcelo EnriqueFORCE-FREEHYPERBOLICEULERhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We 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 noncontinuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaAmerican Physical Society2017-03-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63677Reula, Oscar Alejandro; Rubio, Marcelo Enrique; Ill posedness of force-free electrodynamics in Euler potentials; American Physical Society; Physical Review D; 95; 6; 6-3-2017; 1-130556-28211089-4918CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.95.064005info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.06415info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.064005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:53:22Zoai:ri.conicet.gov.ar:11336/63677instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:53:22.322CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Ill posedness of force-free electrodynamics in Euler potentials
title Ill posedness of force-free electrodynamics in Euler potentials
spellingShingle Ill posedness of force-free electrodynamics in Euler potentials
Reula, Oscar Alejandro
FORCE-FREE
HYPERBOLIC
EULER
title_short Ill posedness of force-free electrodynamics in Euler potentials
title_full Ill posedness of force-free electrodynamics in Euler potentials
title_fullStr Ill posedness of force-free electrodynamics in Euler potentials
title_full_unstemmed Ill posedness of force-free electrodynamics in Euler potentials
title_sort Ill posedness of force-free electrodynamics in Euler potentials
dc.creator.none.fl_str_mv Reula, Oscar Alejandro
Rubio, Marcelo Enrique
author Reula, Oscar Alejandro
author_facet Reula, Oscar Alejandro
Rubio, Marcelo Enrique
author_role author
author2 Rubio, Marcelo Enrique
author2_role author
dc.subject.none.fl_str_mv FORCE-FREE
HYPERBOLIC
EULER
topic FORCE-FREE
HYPERBOLIC
EULER
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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 noncontinuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
description 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 noncontinuous in that norm with respect to the initial data. We furthermore prove that this problem is also ill-posed in the Leray-Ohya sense.
publishDate 2017
dc.date.none.fl_str_mv 2017-03-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/63677
Reula, Oscar Alejandro; Rubio, Marcelo Enrique; Ill posedness of force-free electrodynamics in Euler potentials; American Physical Society; Physical Review D; 95; 6; 6-3-2017; 1-13
0556-2821
1089-4918
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63677
identifier_str_mv Reula, Oscar Alejandro; Rubio, Marcelo Enrique; Ill posedness of force-free electrodynamics in Euler potentials; American Physical Society; Physical Review D; 95; 6; 6-3-2017; 1-13
0556-2821
1089-4918
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.95.064005
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.06415
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.064005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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