The authors give conditions on vorticity guaranteeing the smoothness of weak solutions to the Navier-Stokes system in . Since the pioneering work of Beirao da Veiga, this procedure has been used several times in the work of Kozono, Ogawa, Taniuchi. In a paper of Chae and Choe the conditions of Serrin type are imposed only on two components of vorticity in , while a result of Kozono and Yatsu requires conditions on two components of vorticity in (BMO) and . In this paper, an analogous result is proved in homogeneous Besov spaces .
The main result reads as follows: Let . Suppose be a weak Leray-Hopf solution to the Navier-Stokes system on with solenoidal initial value . Set and assume that
Then is regular provided ; , .