dc.contributor.author | Siljander, Juhana | |
dc.contributor.author | Urbano, José Miguel | |
dc.date.accessioned | 2017-09-01T05:09:13Z | |
dc.date.available | 2018-07-11T21:35:36Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Siljander, 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.other | CONVID_27175692 | |
dc.identifier.other | TUTKAID_74748 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/55237 | |
dc.description.abstract | We 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.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartofseries | Calculus of Variations and Partial Differential Equations | |
dc.subject.other | interior regularity | |
dc.subject.other | weak solutions | |
dc.subject.other | Euler equations | |
dc.title | On the interior regularity of weak solutions to the 2-D incompressible Euler equations | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201708253570 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.date.updated | 2017-08-25T12:15:05Z | |
dc.type.coar | journal article | |
dc.description.reviewstatus | peerReviewed | |
dc.relation.issn | 0944-2669 | |
dc.relation.numberinseries | 5 | |
dc.relation.volume | 56 | |
dc.type.version | acceptedVersion | |
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.accesslevel | openAccess | fi |
dc.subject.yso | matematiikka | |
dc.subject.yso | yhtälöt | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p3160 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p3553 | |
dc.relation.doi | 10.1007/s00526-017-1231-8 | |