Some developments on the global conditional regularity of the Navier-Stokes equations concerning one velocity component
2014
Abstract
The Navier-Stokes system represents well established model for describing flows of viscous incompressible fluids. Although it is widely used in numerous applications, its mathematical analysis is far from being satisfactory.
Recently, there have appeared many regularity criteria for weak solutions regarding one velocity component or/and part of its gradient. The aim of this review note is to give an introduction into this area and an overview of known results.