One component regularity for the Navier–Stokes equations

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Published 22 December 2005 • 2006 IOP Publishing Ltd and London Mathematical Society
, , Citation Igor Kukavica and Mohammed Ziane 2006 Nonlinearity 19 453 DOI 10.1088/0951-7715/19/2/012

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1 Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Dates

  1. Received 27 May 2005
  2. Published

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0951-7715/19/2/453

Abstract

We establish sufficient conditions for the regularity of solutions of the Navier–Stokes system based on conditions on one component of the velocity. The first result states that if , where and 54/23 ⩽ r ⩽ 18/5, then the solution is regular. The second result is that if , where and 24/5 ⩽ r ⩽ ∞, then the solution is regular. These statements improve earlier results on one component regularity.

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10.1088/0951-7715/19/2/012