A REGULARITY CRITERION TO THE 3D BOUSSINESQ EQUATIONS
The paper deals with the regularity criterion for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution (u, theta) becomes regular provided that (del(h)u, del(h)theta) is an element of L-8/3 (0, T; B-infinity,B-infinity (R-3)). Our results improve and extend the well-known results of Fang-Qian  for the Navier-Stokes equations.
Ben Omrane I.2