On the regularity conditions of suitable weak solutions of the 3D navier-stokes equations

摘要

Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier-Stokes equations in a space-time domain containing z0=(x0, t0), and let Qz0,r=Bx0,r × (t0 ?r~2, t0) be a parabolic cylinder in the domain. We show that if either ν × W/|W| ε L ~(γ, α)_(X,t) (Qz0,r) with 3/γ + 2/α ≤ 1, or w × ν/|ν| ε L~(γ, α)_(X,t) 3/γ + 2/α ≤ 2 L~(γ, α)_(X,t) denotes the Serrin type of class, then z _0 is a regular point for ν. This refines previous local regularity criteria for the suitable weak solutions.