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dc.contributor.authorSiljander, Juhana
dc.contributor.authorUrbano, José Miguel
dc.date.accessioned2017-09-01T05:09:13Z
dc.date.available2018-07-11T21:35:36Z
dc.date.issued2017
dc.identifier.citationSiljander, J., & Urbano, J. M. (2017). On the interior regularity of weak solutions to the 2-D incompressible Euler equations. <i>Calculus of Variations and Partial Differential Equations</i>, <i>56</i>(5), Article 126. <a href="https://doi.org/10.1007/s00526-017-1231-8" target="_blank">https://doi.org/10.1007/s00526-017-1231-8</a>
dc.identifier.otherCONVID_27175692
dc.identifier.otherTUTKAID_74748
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/55237
dc.description.abstractWe study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi-Nash-Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result u ∈ L 2+ε loc (ΩT ) =⇒ local regularity for weak solutions in the energy space L∞t L2 x, satisfying appropriate vorticity estimates. We also obtain improved integrability for the vorticity – which is to be compared with the DiPerna-Lions assumptions. The argument is completely local in nature as the result follows from the structural properties of the equation alone, while completely avoiding all sorts of boundary conditions and related gradient estimates. To the best of our knowledge, the approach we follow is new in the context of Euler equations and provides an alternative look at interior regularity issues. We also show how our method can be used to give a modified proof of the classical Serrin condition for the regularity of the Navier-Stokes equations in any dimension.
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesCalculus of Variations and Partial Differential Equations
dc.subject.otherinterior regularity
dc.subject.otherweak solutions
dc.subject.otherEuler equations
dc.titleOn the interior regularity of weak solutions to the 2-D incompressible Euler equations
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201708253570
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.date.updated2017-08-25T12:15:05Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.relation.issn0944-2669
dc.relation.numberinseries5
dc.relation.volume56
dc.type.versionacceptedVersion
dc.rights.copyright© Springer-Verlag GmbH Germany 2017. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.subject.ysomatematiikka
dc.subject.ysoyhtälöt
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
jyx.subject.urihttp://www.yso.fi/onto/yso/p3553
dc.relation.doi10.1007/s00526-017-1231-8


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