Asymptotic Properties Of Solutions Of 3D Viscous Ocean Primitive Equations Driven By Colored Noise

This thesis discusses the wellposedness and long time behavior of the solution of this model driven by colored noise,using a large scale 3D viscous ocean primitive equation system as a prototype.This thesis is divided into two main parts,the first part verifies the wellposedness of the solutions of the system of equations driven by colored noise,and the second part verifies the existence of weak attractors and the conclusion that weak attractors are strong attractors,which are described in detail in Chapters 3 and 4,respectively.First,in Chapter 3,Galerkin’s method is applied to obtain the wellposedness of the strong solutions of the system of equations for individual colornoise driving and linear color-noise driving in the distributional sense obtains the uniqueness and the existence of L∞(t0,T;V)∩L2(t0,T;(H2(Ω))3)space solutions.For the nonlinear case,the same system of equations as in the previous two classes is obtained in the distributional sense satisfying with the local existence uniqueness of the solution.Second,the existence of bounded absorbing sets is obtained in Chapter 4 using the priori estimates made in Chapter 3,and weak asymptotic compactness is obtained from spatial reflexivity,which leads to the existence of weak attractors for the set of equations driven by individual colored noise and linear colored noise.Then using the idea that weak convergence and norm convergence can be introduced to strong convergence,the energy method is applied to verify that the weak attractor is a strong attractor by verifying that lim supn→∞E(vnj(tnj))≤E(v(μ)),which yields norm convergence.