A regularity criterion of weak solutions to the 3D Boussinesq equations

In this note, a regularity criterion of weak solutions to the 3D-Boussinesq equations with respect to Serrin type condition under the framework of Besov space : B-infinity(r),(infinity). It is shown that the weak solution (u; theta) is regular on (0; T] if u satisfies integral(T)(0) parallel to u(center dot, t)parallel to(2/1+r)r(B infinity,infinity) dt < infinity, for 0 < r < 1. This result improves some previous works