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On Kato's method for Navier--Stokes Equations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHAAK, Bernhard H.
hal.structure.identifierINSTITUT FUER ANALYSIS
dc.contributor.authorKUNSTMANN, Peer-Christian
dc.date.accessioned2024-04-04T02:53:01Z
dc.date.available2024-04-04T02:53:01Z
dc.date.created2008-01-17
dc.date.issued2009-12
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192131
dc.description.abstractEnWe investigate Kato's method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier-Stokes equations, our approach unifies several results known in the literature, partly with different proofs. Moreover, we establish new existence and uniqueness results for rough initial data on arbitrary domains in ${\mathbb R}^3$ and irregular domains in ${\mathbb R}^n$.
dc.language.isoen
dc.title.enOn Kato's method for Navier--Stokes Equations
dc.typeArticle de revue
dc.identifier.doi10.1007/s00021-008-0270-5
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv0709.2067
bordeaux.journalJournal of Mathematical Fluid Dynamics
bordeaux.page492-535
bordeaux.volume11
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00281647
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00281647v1
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