On the global regularity for a 3D Boussinesq model without thermal diffusion

In a recent paper (Ye in Z Angew Math Phys 68:83, 2017), Ye proved the global persistence of regularity for a 3D Boussinesq model in $$H^{s}({\mathbb {R}}^3) \times H^{s}({\mathbb {R}}^3)$$ with $$s>5/2$$. In this paper, we show that the global persistence and uniqueness still hold when $$s>3/2$$.