Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations

Abstract

We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two examples concerning the regularity of weak solutions stemming from the regularity of two components of the vorticity ([2]) or from the regularity of the pressure ([3]). We conclude by presenting regularity criteria near the boundary based on the results in [10] and [16].