Well-posedness Of Ocean Dynamic Equations With Topography Effects

The ocean dynamics equations based on the primitive equation and the salinity equation with the new salinity boundary condition are analyzed in this paper.For the initial data with some regularities,the stability and the existence of global weak solutions,the existence of attractors to the ocean dynamics equations are proved by using the energy estimates method.In chapter 1,the ocean dynamic equations with the topographic effects and the nonstationary external forcing are introduced,and some important results of the well-posedness of primitive equations are also given.In chapter 2,the ocean dynamics equations with the topographic effects and the nonstationary external forcing are simplified and the definition of several operators are given.Then the energy estimations of the system are proven,and we show the stability and existence of global weak solutions,and the existence of attractors to the ocean dynamics equations in the case that a new ocean salinity boundary condition is given.In chapter 3,the well-posedness of the ocean dynamic equations with stochastic external forcing is investigated.The Wiener process is introduced,and the definition of stochastic external forcing is addressed.Then a priori estimates of the ocean dynamic equations with stochastic external forcing are established,and we deduce the stability and existence of the weak solution.Finally,the main results of this paper and the future research are given in chapter 4.