Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 66, Issue 8, Pages 1753-1769Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2006.02.043
Keywords
Navier-Stokes equations; regularity; boundary conditions
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We consider the 3D Navier-Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution ('strong' in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity. (c) 2006 Elsevier Ltd. All rights reserved.
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