Local regularity criteria in terms of one velocity component for the Navier-Stokes equations

Abstract

This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point $z$ if its scaled $L_t^p{L}_x^q$-norm of some quantities related to the velocity field is finite and the scaled $L_t^p{L}_x^q$-norm of one velocity component is sufficiently small near $z$.

References in corpus (2)

• Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations
• An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data