Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow

We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr¨odinger map with values on the 2-D sphere, and to the 1-D cubic Schr¨odinger equation. Alth...

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Detalles Bibliográficos
Autores: Banica, V., Vega, L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1609
Acceso en línea:http://hdl.handle.net/20.500.11824/1609
Access Level:acceso abierto
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spelling Unbounded growth of the energy density associated to the Schrödinger map and the binormal flowBanica, V.Vega, L.We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr¨odinger map with values on the 2-D sphere, and to the 1-D cubic Schr¨odinger equation. Although these equations are completely integrable we show the existence of an unbounded growth of the energy density. The density is given by the amplitude of the high frequencies of the derivative of the tangent vectors of the curves, thus giving information of the oscillation at small scales. In the setting of vortex filaments the variation of the tangent vectors is related to the derivative of the direction of the vorticity, that according to the Constantin-Fefferman-Majda criterion plays a relevant role in the possible development of singularities for Euler equations.202320232021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1609reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)InglésReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/16092026-06-19T12:47:47Z
dc.title.none.fl_str_mv Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
title Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
spellingShingle Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
Banica, V.
title_short Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
title_full Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
title_fullStr Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
title_full_unstemmed Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
title_sort Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
dc.creator.none.fl_str_mv Banica, V.
Vega, L.
author Banica, V.
author_facet Banica, V.
Vega, L.
author_role author
author2 Vega, L.
author2_role author
description We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr¨odinger map with values on the 2-D sphere, and to the 1-D cubic Schr¨odinger equation. Although these equations are completely integrable we show the existence of an unbounded growth of the energy density. The density is given by the amplitude of the high frequencies of the derivative of the tangent vectors of the curves, thus giving information of the oscillation at small scales. In the setting of vortex filaments the variation of the tangent vectors is related to the derivative of the direction of the vorticity, that according to the Constantin-Fefferman-Majda criterion plays a relevant role in the possible development of singularities for Euler equations.
publishDate 2021
dc.date.none.fl_str_mv 2021
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1609
url http://hdl.handle.net/20.500.11824/1609
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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