REGULARITY OF NAVIER-STOKES EQUATIONS

摘要

The purpose of this article is to show that a weak solution to the Navier-Stokes equations (NSE) in an infinite channel or in a spherical domain is actually regular up to the boundary if one component of the velocity is smooth enough. As a novelty, the 3D NSE are viewed as a perturbation of the 2D NSE in a sense to be explained below.