Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher

Building on the work of Crouseilles and Faou on the 2D case, we construct quasi-periodic solutions to the incompressible Euler equations with periodic boundary conditions in dimension 3 and in any even dimension. These solutions are genuinely high-dimensional, which is particularly interesting becau...

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Detalhes bibliográficos
Autores: Enciso, Alberto, Peralta Salas, Daniel, Torres de Lizaur, Francisco
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/181136
Acesso em linha:https://hdl.handle.net/11441/181136
https://doi.org/10.1016/j.jde.2023.01.013
Access Level:acceso abierto
Palavra-chave:Incompressible Euler equations
Quasi-periodic solutions
Compactly supported steady states
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spelling Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higherEnciso, AlbertoPeralta Salas, DanielTorres de Lizaur, FranciscoIncompressible Euler equationsQuasi-periodic solutionsCompactly supported steady statesBuilding on the work of Crouseilles and Faou on the 2D case, we construct quasi-periodic solutions to the incompressible Euler equations with periodic boundary conditions in dimension 3 and in any even dimension. These solutions are genuinely high-dimensional, which is particularly interesting because there are extremely few examples of high-dimensional initial data for which global solutions are known to exist. These quasi-periodic solutions can be engineered so that they are dense on tori of arbitrary dimension embedded in the space of solenoidal vector fields. Furthermore, in the two-dimensional case we show that quasi-periodic solutions are dense in the phase space of the Euler equations. More precisely, for any integer we prove that any initial stream function can be approximated in (strongly when and weak-⁎ when ) by smooth initial data whose solutions are dense on N-dimensional tori.ElsevierAnálisis Matemático2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/181136https://doi.org/10.1016/j.jde.2023.01.013reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Differential Equations, 354, 170-182.10.1016/j.jde.2023.01.013info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1811362026-06-17T12:51:07Z
dc.title.none.fl_str_mv Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
title Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
spellingShingle Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
Enciso, Alberto
Incompressible Euler equations
Quasi-periodic solutions
Compactly supported steady states
title_short Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
title_full Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
title_fullStr Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
title_full_unstemmed Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
title_sort Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher
dc.creator.none.fl_str_mv Enciso, Alberto
Peralta Salas, Daniel
Torres de Lizaur, Francisco
author Enciso, Alberto
author_facet Enciso, Alberto
Peralta Salas, Daniel
Torres de Lizaur, Francisco
author_role author
author2 Peralta Salas, Daniel
Torres de Lizaur, Francisco
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
dc.subject.none.fl_str_mv Incompressible Euler equations
Quasi-periodic solutions
Compactly supported steady states
topic Incompressible Euler equations
Quasi-periodic solutions
Compactly supported steady states
description Building on the work of Crouseilles and Faou on the 2D case, we construct quasi-periodic solutions to the incompressible Euler equations with periodic boundary conditions in dimension 3 and in any even dimension. These solutions are genuinely high-dimensional, which is particularly interesting because there are extremely few examples of high-dimensional initial data for which global solutions are known to exist. These quasi-periodic solutions can be engineered so that they are dense on tori of arbitrary dimension embedded in the space of solenoidal vector fields. Furthermore, in the two-dimensional case we show that quasi-periodic solutions are dense in the phase space of the Euler equations. More precisely, for any integer we prove that any initial stream function can be approximated in (strongly when and weak-⁎ when ) by smooth initial data whose solutions are dense on N-dimensional tori.
publishDate 2023
dc.date.none.fl_str_mv 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 https://hdl.handle.net/11441/181136
https://doi.org/10.1016/j.jde.2023.01.013
url https://hdl.handle.net/11441/181136
https://doi.org/10.1016/j.jde.2023.01.013
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Differential Equations, 354, 170-182.
10.1016/j.jde.2023.01.013
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
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repository.mail.fl_str_mv
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