Abstract
In this note, we are devoted to study the conditional regularity for the three dimensional Navier-Stokes in terms of the Morrey and BMO spaces. More precisely, we show that if u is a weak solution and u(3) is an element of L-2 (0, T; BMO(R-3)) and omega(3) is an element of L2/2-r(0, T; M-2,M-3/r(R-3)) with 0 < r < 1, then u is regular on (0, T]. This improves the available result by Zhang (2018) with u(3) is an element of L-2(0, T; L-infinity(R-3)) and omega(3) is an element of L2/2-r(0, T; L-3/r(R-3)) with 0 < r < 1.