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

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    RegularityCriterion3DNavier.pdf (111.6Kb)
    Date
    2009-02
    Author
    Vasseur, Alexis
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    Abstract
    In 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.
    Department
    Mathematics
    Subject
    navier-stokes
    fluid mechanics
    regularity
    prodi-serrin criteria
    mathematics, applied
    URI
    http://hdl.handle.net/2152/31160
    xmlui.dri2xhtml.METS-1.0.item-citation
    Vasseur, 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-y
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