Rigidity of acute angled corners for one phase Muskat interfaces

We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle co...

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Detalles Bibliográficos
Autores: Agrawal, Siddhant, Patel, Neel, Wu, Sijue
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/349474
Acceso en línea:http://hdl.handle.net/10261/349474
https://api.elsevier.com/content/abstract/scopus_id/85143870919
Access Level:acceso abierto
Palabra clave:Muskat equation
Rigidity
Singularities
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spelling Rigidity of acute angled corners for one phase Muskat interfacesAgrawal, SiddhantPatel, NeelWu, SijueMuskat equationRigiditySingularitiesWe consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle corners or cusps. Moreover, we show that isolated corners/cusps on the interface must be rigid, meaning the angle of the corner is preserved for a finite time, there is no rotation at the tip, the particle at the tip remains at the tip and the velocity of that particle at the tip points vertically downward.We are very grateful to Inwon Kim for explaining to us the equivalence of the one phase Muskat equation and the Hele Shaw problem with injection at infinity in an infinite domain. Siddhant Agrawal was partially supported by the National Science Foundation under Grant No. DMS-1928930 while participating in a program hosted by MSRI during the Spring 2021 semester. Neel Patel was partially supported by an AMS-Simons Travel Grant, which are administered by the American Mathematical Society with support from the Simons Foundation. Sijue Wu is supported in part by NSF grant DMS-1764112. She was also supported by NSF grant DMS-1928930 through the program on Mathematical problems in fluid dynamics at MSRI during the Spring 2021 semester.Peer reviewedConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202420242023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/349474https://api.elsevier.com/content/abstract/scopus_id/85143870919reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésAdvances in Mathematicshttps://www.sciencedirect.com/science/article/pii/S0001870822006181Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3494742026-05-22T06:33:51Z
dc.title.none.fl_str_mv Rigidity of acute angled corners for one phase Muskat interfaces
title Rigidity of acute angled corners for one phase Muskat interfaces
spellingShingle Rigidity of acute angled corners for one phase Muskat interfaces
Agrawal, Siddhant
Muskat equation
Rigidity
Singularities
title_short Rigidity of acute angled corners for one phase Muskat interfaces
title_full Rigidity of acute angled corners for one phase Muskat interfaces
title_fullStr Rigidity of acute angled corners for one phase Muskat interfaces
title_full_unstemmed Rigidity of acute angled corners for one phase Muskat interfaces
title_sort Rigidity of acute angled corners for one phase Muskat interfaces
dc.creator.none.fl_str_mv Agrawal, Siddhant
Patel, Neel
Wu, Sijue
author Agrawal, Siddhant
author_facet Agrawal, Siddhant
Patel, Neel
Wu, Sijue
author_role author
author2 Patel, Neel
Wu, Sijue
author2_role author
author
dc.contributor.none.fl_str_mv Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Muskat equation
Rigidity
Singularities
topic Muskat equation
Rigidity
Singularities
description We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle corners or cusps. Moreover, we show that isolated corners/cusps on the interface must be rigid, meaning the angle of the corner is preserved for a finite time, there is no rotation at the tip, the particle at the tip remains at the tip and the velocity of that particle at the tip points vertically downward.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/349474
https://api.elsevier.com/content/abstract/scopus_id/85143870919
url http://hdl.handle.net/10261/349474
https://api.elsevier.com/content/abstract/scopus_id/85143870919
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Advances in Mathematics
https://www.sciencedirect.com/science/article/pii/S0001870822006181
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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