| Abstract: |
| In this talk, we consider 3D anisotropic Boussinesq equations with horizontal dissipation. We prove that, for the perturbed equations, the time global solution exists for small initial data in the anisotropic Sobolev spaces $H^{0,s}$ with $\frac 12 < s$ and the corresponding solution of the unperturbed equations approaches the hydrostatic equilibrium. Moreover, the optimal decay result is obtained in the anisotropic Sobolev spaces $H^{0,s}$, extending the result of isotropic Sobolev spaces. |
|