On the Regularity Conditions of Suitable Weak Solutions of the 3D Navier-Stokes Equations

초록

Let v and ! be the velocity and the vorticity of the a suitable weak solution of the 3D Navier-Stokes equations in a space- time domain containing z(0)=(x(0), t(0)), and let Q(z0), r = Bx(0), r x (t(0) - r(2), t(0)) be a parabolic cylinder in the domain. We show that if either nu x omega/vertical bar omega vertical bar is an element of L-x,t(gamma,alpha) (Qz(0), r) with (3)(gamma) + (2)(alpha) <= 1, or omega x (nu)(vertical bar nu vertical bar) is an element of L-x,t(gamma,alpha) (Q(z0), (r)) with (3)(gamma) + (2)(alpha) <= 2, where L-x,t(gamma,alpha) denotes the Serrin type of class, then z(0) is a regular point for nu. This refines previous local regularity criteria for the suitable weak solutions.

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