The exponential behavior of the stochastic three-dimensional primitive equations with multiplicative noise (Q619705)

The author studies the stability of weak solutions to the stochastic 3D primitive equations with multiplicative noise. The 3D primitive equations of the ocean are derived from the Navier-Stokes equations, with Coriolis force, coupled with the thermodynamic equation for the salinity. The author proves that the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions under some restrictions on the viscosity and the forcing terms. Applying the Itô formula, the author studies the stability of stationary solutions to the stochastic 3D primitive equations. It is also proved a result related to the stabilization of these equations.