Ergodicity for two class stochastic partial differential equations with anisotropic viscosity

We prove the ergodicity on anisotropic space ??????0,1 for two class stochastic PDEs with anisotropic viscosity: the Navier-Stokes equations, the primitive equations. The Maslowski-Seidler theory and an asymptotic coupling argument are invoked to overcome several aspects challenges causing by the fact that systems only have partial dissipation and the strong nonlinearity construction.