A mathematical theory of isolated systems in relativistic plasma physics

Detalhes bibliográficos
Autor(a) principal: Calogero, Simone Carmelo
Data de Publicação: 2007
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/6583
Resumo: The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the mass-energy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the mass-energy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the mass-energy on the forward hyperboloids is non-increasing and uniformly bounded by the mass-energy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one dimensional version of the system.
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spelling A mathematical theory of isolated systems in relativistic plasma physicsVlasov-maxwellInitial valueIncoming radiationIsolated solutionsProblem hyperboloidisolated solutioninitial value problembackward hyperboloidoutgoing radiationScience & TechnologyThe existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the mass-energy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the mass-energy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the mass-energy on the forward hyperboloids is non-increasing and uniformly bounded by the mass-energy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one dimensional version of the system.Fundação para a Ciência e a Tecnologia (FCT)World Scientific PublishingUniversidade do MinhoCalogero, Simone Carmelo2007-062007-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/6583eng"Journal of hyperbolic differential equations". ISSN 0219-8916. 4:2 (June 2007) 267-294.0219-8916http://www.worldscinet.cominfo: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:RCAAP2023-07-21T12:19:05Zoai:repositorium.sdum.uminho.pt:1822/6583Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:12:00.237094Repositório 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 A mathematical theory of isolated systems in relativistic plasma physics
title A mathematical theory of isolated systems in relativistic plasma physics
spellingShingle A mathematical theory of isolated systems in relativistic plasma physics
Calogero, Simone Carmelo
Vlasov-maxwell
Initial value
Incoming radiation
Isolated solutions
Problem hyperboloid
isolated solution
initial value problem
backward hyperboloid
outgoing radiation
Science & Technology
title_short A mathematical theory of isolated systems in relativistic plasma physics
title_full A mathematical theory of isolated systems in relativistic plasma physics
title_fullStr A mathematical theory of isolated systems in relativistic plasma physics
title_full_unstemmed A mathematical theory of isolated systems in relativistic plasma physics
title_sort A mathematical theory of isolated systems in relativistic plasma physics
author Calogero, Simone Carmelo
author_facet Calogero, Simone Carmelo
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Calogero, Simone Carmelo
dc.subject.por.fl_str_mv Vlasov-maxwell
Initial value
Incoming radiation
Isolated solutions
Problem hyperboloid
isolated solution
initial value problem
backward hyperboloid
outgoing radiation
Science & Technology
topic Vlasov-maxwell
Initial value
Incoming radiation
Isolated solutions
Problem hyperboloid
isolated solution
initial value problem
backward hyperboloid
outgoing radiation
Science & Technology
description The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the mass-energy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the mass-energy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the mass-energy on the forward hyperboloids is non-increasing and uniformly bounded by the mass-energy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one dimensional version of the system.
publishDate 2007
dc.date.none.fl_str_mv 2007-06
2007-06-01T00:00:00Z
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/1822/6583
url http://hdl.handle.net/1822/6583
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Journal of hyperbolic differential equations". ISSN 0219-8916. 4:2 (June 2007) 267-294.
0219-8916
http://www.worldscinet.com
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
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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