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 satisfies The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.
"A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space." Abstr. Appl. Anal. 2012 1 - 9, 2012. https://doi.org/10.1155/2012/184674