, Volume 273, Issue 1, pp 161-176

Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

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Abstract

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled ${L^{p,q}_{x,t}}$ -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the ${L^{p,q}_{x,t}}$ -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤  q <  ∞, or the ${L^{p,q}_{x,t}}$ -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤  q, 1 ≤  p, is sufficiently small near z.

Communicated by P. Constantin