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dc.contributor.authorAmbrosio, Luigi
dc.contributor.authorNicolussi Golo, Sebastiano
dc.contributor.authorSerra Cassano, Francesco
dc.date.accessioned2023-08-30T09:55:43Z
dc.date.available2023-08-30T09:55:43Z
dc.date.issued2023
dc.identifier.citationAmbrosio, L., Nicolussi Golo, S., & Serra Cassano, F. (2023). Classical flows of vector fields with exponential or sub-exponential summability. <i>Journal of Differential Equations</i>, <i>372</i>(5), 458-504. <a href="https://doi.org/10.1016/j.jde.2023.07.005" target="_blank">https://doi.org/10.1016/j.jde.2023.07.005</a>
dc.identifier.otherCONVID_184006724
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/88801
dc.description.abstractWe show that vector fields b whose spatial derivative Dx b satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin (N) condition in a quantitative form, too. Furthermore, we prove that if Dx b satisfies a suitable exponential summability condition then the flow associated to b has Sobolev regularity, without assuming boundedness of divx b. We then apply these results to the representation and Sobolev regularity of weak solutions of the Cauchy problem for the transport and continuity equations.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier BV
dc.relation.ispartofseriesJournal of Differential Equations
dc.rightsCC BY 4.0
dc.subject.othervector fields
dc.subject.otherflow
dc.subject.otherSobolev–Orlicz spaces
dc.subject.othertransport equation
dc.subject.othercontinuity equation
dc.titleClassical flows of vector fields with exponential or sub-exponential summability
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202308304838
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange458-504
dc.relation.issn0022-0396
dc.relation.numberinseries5
dc.relation.volume372
dc.type.versionpublishedVersion
dc.rights.copyright© 2023 The Authors. Published by Elsevier Inc.
dc.rights.accesslevelopenAccessfi
dc.subject.ysodifferentiaaliyhtälöt
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p3552
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1016/j.jde.2023.07.005
dc.type.okmA1


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