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Global regularity for the Navier-Stokes equations with some classes of large initial data

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAICU, Marius
hal.structure.identifierSchool of Mathematical Sciences, Peking University, 100871, P. R. China
dc.contributor.authorZHANG, Zhifei
dc.date.accessioned2024-04-04T02:17:21Z
dc.date.available2024-04-04T02:17:21Z
dc.date.issued2011
dc.identifier.issn2157-5045
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189220
dc.description.abstractEnChemin, Gallagher, and Paicu obtained in 2010 a class of large initial data that generate a global smooth solution to the three-dimensional, incompressible Navier-Stokes equation. The data varies slowly in the vertical direction -- it is expressed as a function of $\epsilon x_3$ -- and it has a norm that blows up as the small parameter goes to zero. This type of initial data can be regarded as an ill prepared case, in contrast with the well prepared case treated in earlier papers. The data was supposed to evolve in a special domain, namely $\Omega=T^2_h\times \R_v$. The choice of a periodic domain in the horizontal variable played an important role. The aim of this article is to study the case where the fluid evolves in the whole space $\R^3$. In this case, we have to overcome the difficulties coming from very low horizontal frequencies. We consider in this paper an intermediate situation between the well prepared case and ill prepared situation (the norms of the horizontal components of initial data are small but the norm of the vertical component blows up as the small parameter goes to zero). The proof uses the analytical-type estimates and the special structure of the nonlinear term of the equation.
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.title.enGlobal regularity for the Navier-Stokes equations with some classes of large initial data
dc.typeArticle de revue
dc.identifier.doi10.2140/apde.2011.4.95
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
bordeaux.journalAnalysis & PDE
bordeaux.page95-113
bordeaux.volume4
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00994726
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00994726v1
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