DC FieldValueLanguage
dc.contributor.authorGabel, Fabian Nuraddin Alexander-
dc.contributor.authorTolksdorf, Patrick-
dc.date.accessioned2022-05-18T11:24:47Z-
dc.date.available2022-05-18T11:24:47Z-
dc.date.issued2022-12-15-
dc.identifier.citationJournal of Differential Equations 340: 227-272 (2022-12-15)de_DE
dc.identifier.issn0022-0396de_DE
dc.identifier.urihttp://hdl.handle.net/11420/12669-
dc.description.abstractWe consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain Ω subject to homogeneous Dirichlet boundary conditions. We prove Lᵖ-resolvent estimates for p satisfying 1 / p - 1 / 2 < 1 / 4 + ε for some ε > 0. We further show that the Stokes operator admits the property of maximal regularity and that its H∞-calculus is bounded. This is then used to characterize domains of fractional powers of the Stokes operator. Finally, we give an application to the regularity theory of weak solutions to the Navier-Stokes equations in bounded planar Lipschitz domains.-
dc.description.abstractWe consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain Ω subject to homogeneous Dirichlet boundary conditions. We prove Lᵖ-resolvent estimates for p satisfying 1 / p - 1 / 2 < 1 / 4 + ε for some ε > 0. We further show that the Stokes operator admits the property of maximal regularity and that its H∞-calculus is bounded. This is then used to characterize domains of fractional powers of the Stokes operator. Finally, we give an application to the regularity theory of weak solutions to the Navier-Stokes equations in bounded planar Lipschitz domains.en
dc.language.isoende_DE
dc.relation.ispartofJournal of differential equationsde_DE
dc.subjectAnalysis of PDEs-
dc.subjectFunctional Analysis-
dc.subjectPrimary 47D06, 35Q30, Secondary 76D03, 76D05, 76D07-
dc.subject.ddc510: Mathematik-
dc.titleThe Stokes operator in two-dimensional bounded Lipschitz domainsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishWe consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain Ω subject to homogeneous Dirichlet boundary conditions. We prove Lᵖ-resolvent estimates for p satisfying 1 / p - 1 / 2 < 1 / 4 + ε for some ε > 0. We further show that the Stokes operator admits the property of maximal regularity and that its H∞-calculus is bounded. This is then used to characterize domains of fractional powers of the Stokes operator. Finally, we give an application to the regularity theory of weak solutions to the Navier-Stokes equations in bounded planar Lipschitz domains.de_DE
tuhh.publisher.doi10.1016/j.jde.2022.09.001-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.volume340de_DE
tuhh.container.startpage227de_DE
tuhh.container.endpage272de_DE
dc.identifier.arxiv2204.05867v1de_DE
dc.identifier.scopus2-s2.0-85137733368de_DE
local.status.inpressfalse-
local.publisher.peerreviewedfalse-
datacite.resourceTypeArticle-
datacite.resourceTypeGeneralJournalArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorOrcidGabel, Fabian Nuraddin Alexander-
item.creatorOrcidTolksdorf, Patrick-
item.creatorGNDGabel, Fabian Nuraddin Alexander-
item.creatorGNDTolksdorf, Patrick-
item.openairetypeArticle-
item.grantfulltextnone-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-8053-0284-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
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