A remark on the regularity criterion of Boussinesq equations with zero heat conductivity

In this note, we consider the regularity problem under the critical condition to the Boussinesq equations with zero heat conductivity. The Serrin type regularity criteria are established in terms of the critical Besov spaces. This improves a result established in a recent work by Geng and Fan (2012) [6]. (C) 2013 Elsevier Ltd. All rights reserved.