Dissipative Euler Flows Originating from Circular Vortex Filaments

In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in C([0, T], L2-). The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and mov...

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Detalles Bibliográficos
Autores: Gancedo García, Francisco, Hidalgo Torné, Antonio, Mengual Bretón, Francisco José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/181745
Acceso en línea:https://hdl.handle.net/11441/181745
https://doi.org/10.1007/s40818-025-00211-5
Access Level:acceso abierto
Palabra clave:Incompressible fluid
Euler equations
Navier-Stokes
Vortex filaments
Convex integration
Axial symmetry
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spelling Dissipative Euler Flows Originating from Circular Vortex FilamentsGancedo García, FranciscoHidalgo Torné, AntonioMengual Bretón, Francisco JoséIncompressible fluidEuler equationsNavier-StokesVortex filamentsConvex integrationAxial symmetryIn this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in C([0, T], L2-). The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space.SpringerAnálisis MatemáticoFQM104: Análisis Matemático2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/181745https://doi.org/10.1007/s40818-025-00211-5reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnals of PDE, 11 (2), 24-1.10.1007/s40818-025-00211-5info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1817452026-06-17T12:51:07Z
dc.title.none.fl_str_mv Dissipative Euler Flows Originating from Circular Vortex Filaments
title Dissipative Euler Flows Originating from Circular Vortex Filaments
spellingShingle Dissipative Euler Flows Originating from Circular Vortex Filaments
Gancedo García, Francisco
Incompressible fluid
Euler equations
Navier-Stokes
Vortex filaments
Convex integration
Axial symmetry
title_short Dissipative Euler Flows Originating from Circular Vortex Filaments
title_full Dissipative Euler Flows Originating from Circular Vortex Filaments
title_fullStr Dissipative Euler Flows Originating from Circular Vortex Filaments
title_full_unstemmed Dissipative Euler Flows Originating from Circular Vortex Filaments
title_sort Dissipative Euler Flows Originating from Circular Vortex Filaments
dc.creator.none.fl_str_mv Gancedo García, Francisco
Hidalgo Torné, Antonio
Mengual Bretón, Francisco José
author Gancedo García, Francisco
author_facet Gancedo García, Francisco
Hidalgo Torné, Antonio
Mengual Bretón, Francisco José
author_role author
author2 Hidalgo Torné, Antonio
Mengual Bretón, Francisco José
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM104: Análisis Matemático
dc.subject.none.fl_str_mv Incompressible fluid
Euler equations
Navier-Stokes
Vortex filaments
Convex integration
Axial symmetry
topic Incompressible fluid
Euler equations
Navier-Stokes
Vortex filaments
Convex integration
Axial symmetry
description In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in C([0, T], L2-). The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space.
publishDate 2025
dc.date.none.fl_str_mv 2025
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/11441/181745
https://doi.org/10.1007/s40818-025-00211-5
url https://hdl.handle.net/11441/181745
https://doi.org/10.1007/s40818-025-00211-5
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annals of PDE, 11 (2), 24-1.
10.1007/s40818-025-00211-5
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 Springer
publisher.none.fl_str_mv Springer
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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