#### Vol. 288, No. 1, 2017

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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 $\Pi =\frac{1}{2}|u{|}^{2}+p$. By the rotation form of the Navier–Stokes equations, we also obtain regularity criteria for suitable weak solutions in terms of either $u×\omega ∕|\omega |$ or $\omega ×u∕|u|$ 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