We address the regularity for the 2D Boussinesq equations with zero diffusivity and positive viscosity on an open bounded smooth domain Ω. In particular, we prove that for the initial velocity in H2(Ω) and the initial density in H1(Ω) there exists a global in time solution for which the velocity and the density are locally in time bounded functions in H2 and H1, respectively.
Bibliographical noteFunding Information:
I.K. was supported in part by the NSF Grant No. DMS-1311943, while M.Z. was supported in part by the NSF Grant No. DMS-1109562. The authors thank the referee for useful suggestions which improved the exposition considerably.
Copyright 2013 Elsevier B.V., All rights reserved.