A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space - Xunwu Yin (Abstract and Applied Analysis)
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 ũ=(u1,u2,0) satisfies ũ(x,t)∈Lq(0,T;Lp,∞(R3))  for  2/q + 3/p=1,  3<p<∞. The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.