Wong-Zakai Approximations Of 3D Stochastic Viscous Primitive Equations And Its Long Time Behavior

The primitive equations(PEs)can be used to explain and modify the large scale oceanic as well as atmospheric dynamics.Such equations have received much attention due to their potential applications in weather prediction,oceangoing,understanding in Earth’s climate system and so forth.The existence and asymptotic behaviors of solutions of deterministic PEs and stochastic PEs with linear white noise have been investigated by many experts.However,for stochastic PEs driven by nonlinear white noise,there is no method available to transform such system into pathwise deterministic systems so far.Therefore,it is not able to deal with such systems with nonlinear noises by the theory of random dynamic system.In this paper,we will consider the WongZakai approximation of stochastic PEs with nonlinear white noise and study its asymptotic behaviors.This paper is organized as follows:In Chapter 1,we introduce the background of PEs and the Wong-Zakai approximation system of 3D stochastic viscous PEs.In Chapter 2,we first discuss the well-posedness of the Wong-Zakai approximation system and prove its uniform estimates.And then,we prove that solutions to the Wong-Zakai approximation system depend continuously on the initial data.Based on this,we show that solution maps of the Wong-Zakai approximation system can generate a continuous cocycle.In Chapter 3,we first introduce some basic theory about random attractors of non-autonomous random dynamical systems.Then we prove the existence of D-pullback absorbing sets of the above continuous cocycle as well as the Dpullback asymptotic compactness,which lead to the existence and uniqueness of D-pullback random attractors.