| Abstract: |
| We present a geometric regularity criterion for the Navier-Stokes equations in the whole three dimensional space. We prove as our main result that the regularity of Leray weak solutions follows from the Lipschitz continuity assumption on the direction of the velocity. Our result is reminiscent of the paper by Constantin and Fefferman who proved the regularity in terms of the direction of the vorticity.
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L.C.Berselli, Some geometric constraints and the problem of global regularity for the
Navier-Stokes equations, Nonlinearity Vol.22, 2009, 2561--2581.
P.Constantin, C.Fefferman: Direction of vorticity and the problem of global regularity for the
Navier-Stokes equations, Indiana Univ. Math. J. Vol. 42, 1993, 775--789. |
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