A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space

Abstract

This paper is concerned with the regularity of Leray weak solutions to the 3D Navier-Stokes equations in Lorentz space. It is proved that the weak solution is regular if the horizontal velocity denoted by $\tilde{u}=(u_1,u_2,0)$ satisfies The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.