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

DOI: 10.2140/pjm.2017.288.189

Abstract

We establish new regularity criteria for suitable weak solutions involving Bernoulli (total) pressure $\Pi =\frac{1}{2}|u{|}^2+p$. By the rotation form of the Navier–Stokes equations, we also obtain regularity criteria for suitable weak solutions in terms of either $u\times \omega ∕\left|\omega \right|$ or $\omega \times u∕\left|u\right|$ with sufficiently small local scaled norm, where $\omega$ 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