Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

Details Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

2006-07-05

arxiv.org/abs/math/0607114v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00220-007-0214-6

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 $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$.

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