On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity

Detalhes bibliográficos
Autor(a) principal: Barros, Vanessa
Data de Publicação: 2022
Outros Autores: Correia, Simão, Oliveira, Filipe
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/29130
Resumo: We study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.
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spelling On the nonlinear Schrödinger equation in spaces of infinite mass and low regularityNonlinear Schrödinger EquationLocal Well-PosednessWe study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.Project euclidRepositório da Universidade de LisboaBarros, VanessaCorreia, SimãoOliveira, Filipe2023-10-26T10:54:56Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29130engBarros, Vanessa; Simão Correia and Filipe Oliveira .(2022). “On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity”. Differential and Integral Equations, Volume 148, No. 2: pp. 371-392metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-29T01:30:54Zoai:www.repository.utl.pt:10400.5/29130Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:26:05.835628Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
title On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
spellingShingle On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
Barros, Vanessa
Nonlinear Schrödinger Equation
Local Well-Posedness
title_short On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
title_full On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
title_fullStr On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
title_full_unstemmed On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
title_sort On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
author Barros, Vanessa
author_facet Barros, Vanessa
Correia, Simão
Oliveira, Filipe
author_role author
author2 Correia, Simão
Oliveira, Filipe
author2_role author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Barros, Vanessa
Correia, Simão
Oliveira, Filipe
dc.subject.por.fl_str_mv Nonlinear Schrödinger Equation
Local Well-Posedness
topic Nonlinear Schrödinger Equation
Local Well-Posedness
description We study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01T00:00:00Z
2023-10-26T10:54:56Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/29130
url http://hdl.handle.net/10400.5/29130
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Barros, Vanessa; Simão Correia and Filipe Oliveira .(2022). “On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity”. Differential and Integral Equations, Volume 148, No. 2: pp. 371-392
dc.rights.driver.fl_str_mv metadata only access
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rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Project euclid
publisher.none.fl_str_mv Project euclid
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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