Vol. 288, No. 1, 2017

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ISSN: 0030-8730
Regularity conditions for suitable weak solutions of the Navier–Stokes system from its rotation form

Changxing Miao and Yanqing Wang

Vol. 288 (2017), No. 1, 189–215
Abstract

We establish new regularity criteria for suitable weak solutions involving Bernoulli (total) pressure Π = 1 2|u|2 + p. By the rotation form of the Navier–Stokes equations, we also obtain regularity criteria for suitable weak solutions in terms of either u × ω|ω| or ω × u|u| with sufficiently small local scaled norm, where ω is the vorticity of the velocity. As a consequence, we extend and refine some known interior regularity criteria for suitable weak solutions.

Keywords
Navier–Stokes equations, suitable weak solutions, regularity, Bernoulli pressure, rotation
Mathematical Subject Classification 2010
Primary: 35B65, 35Q30
Milestones
Received: 4 January 2016
Revised: 24 July 2016
Accepted: 28 September 2016
Published: 8 April 2017
Authors
Changxing Miao
Institute of Applied Physics and Computational Mathematics
P. O. Box 8009
100088 Beijing
China
Yanqing Wang
Department of Mathematics and Information Science
Zhengzhou University of Light Industry
450002 Zhengzhou
China