Regularity Criterion For 3D Navier-Stokes Equations In Terms Of The Direction Of The Velocity

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dc.contributor.utaustinauthorVasseur, Alexisen
dc.creatorVasseur, Alexisen
dc.date.accessioned2015-09-09T15:51:01Zen
dc.date.available2015-09-09T15:51:01Zen
dc.date.issued2009-02en
dc.description.abstractIn this short note we give a link between the regularity of the solution u to the 3D Navier-Stokes equation and the behavior of the direction of the velocity u/|u|. It is shown that the control of div(u/vertical bar u vertical bar) in a suitable L (t/p) (L (x/q) ) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based on very standard methods, relies on a straightforward relation between the divergence of the direction of the velocity and the growth of energy along streamlines.en
dc.description.departmentMathematicsen
dc.description.sponsorshipen
dc.identifier.citationVasseur, Alexis. Regularity Criterion For 3D Navier-Stokes Equations In Terms Of The Direction Of The Velocity. Applications of Mathematics, Volume 54, Issue 1, (Feb., 2009) pp 47-52. DOI: 10.1007/s10492-009-0003-yen
dc.identifier.doi10.1007/s10492-009-0003-yen
dc.identifier.issn0862-7940en
dc.identifier.urihttp://hdl.handle.net/2152/31160en
dc.identifier.urlen
dc.language.isoEnglishen
dc.relation.ispartofserialApplications of Mathematicsen
dc.rightsAdministrative deposit of works to Texas ScholarWorks: This works author(s) is or was a University faculty member, student or staff member; this article is already available through open access or the publisher allows a PDF version of the article to be freely posted online. The library makes the deposit as a matter of fair use (for scholarly, educational, and research purposes), and to preserve the work and further secure public access to the works of the University.en
dc.rights.holderen
dc.subjectnavier-stokesen
dc.subjectfluid mechanicsen
dc.subjectregularityen
dc.subjectprodi-serrin criteriaen
dc.subjectmathematics, applieden
dc.titleRegularity Criterion For 3D Navier-Stokes Equations In Terms Of The Direction Of The Velocityen
dc.typeArticleen

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