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STRIATED REGULARITY OF 2-D INHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES SYSTEM WITH VARIABLE VISCOSITY

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAICU, Marius
hal.structure.identifierAcadémie Chinoise des Sciences
dc.contributor.authorZHANG, Ping
dc.date2020
dc.date.accessioned2024-04-04T02:55:39Z
dc.date.available2024-04-04T02:55:39Z
dc.date.issued2020
dc.identifier.issn0010-3616
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192385
dc.description.abstractEnIn this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L 1 in time Lipschitz estimate of the velocity field can not be obtained by energy method (see [11, 20, 21] for instance). Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid ([6, 7]), namely, striated regularity can help to get the L ∞ boundedness of the double Riesz transform, we derive the a priori L 1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space. As an application, we shall prove the propagation of H 3 regularity of the interface between fluids with different densities.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enInhomogeneous Navier-Stokes equations
dc.subject.enLittlewood-Paley theory
dc.subject.enStriated regularity
dc.title.enSTRIATED REGULARITY OF 2-D INHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES SYSTEM WITH VARIABLE VISCOSITY
dc.typeArticle de revue
dc.identifier.doi10.1007/s00220-019-03446-z
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
bordeaux.journalCommunications in Mathematical Physics
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02501816
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02501816v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Mathematical%20Physics&rft.date=2020&rft.eissn=0010-3616&rft.issn=0010-3616&rft.au=PAICU,%20Marius&ZHANG,%20Ping&rft.genre=article


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