On the Interior Regularity of Suitable Weak Solutions to the Navier–Stokes Equations

Abstract

We obtain the interior regularity criteria for the vorticity of “suitable” weak solutions to the Navier–Stokes equations. We prove that if two components of a vorticiy belongs to in a neighborhood of an interior point with 3/p + 2/q ≤ 2 and 3/2 < p < ∞, then solution is regular near that point. We also show that if the direction field of the vorticity is in some Triebel–Lizorkin spaces and the vorticity magnitude satisfies an appropriate integrability condition in a neighborhood of a point, then solution is regular near that point.