Stability and large-time behavior of the 2D Boussinesq system with mixed
partial dissipations near hydrostatic equilibrium
The purpose of this note is to address the stability and large-time
behavior for the 2D Boussinesq system with vertical dissipation on
$u_1$ and horizontal dissipation on $u_2$ near a hydrostatic
equilibrium. Meanwhile the decay estimates of that system are also
presented. Finally, we also obtain the decay rates of the solution to
the corresponding linearized equation of the Boussinesq system.