First, we consider three dimensional incompressible Navier-Stokes equations with fractional dissipation and Coriolis force. We find Coriolis force gives extra temporal decay of the solutions under some conditions on the initial data.
Next, we consider the three-dimensional damped Boussinesq equations with strong stratification. We find the global-in-time existence of solutions under some conditions of the initial data and the temporal decay of solutions.
This is based on the joint work with Jaewook Ahn(Dongguk Univ.) and Junha Kim(Chung-Ang Univ.).