On The Well-posedness Of The Initial Boundary Value Problems To Moist Atmospheric Equations With Random External Forcing

The moist atmospheric equations are nonlinear equations coupled by the velocity field equations,temperature equation,specific humidity equation and liquid water content equation.In this paper,the existence and stability of the global weak solution,the existence and uniqueness of the global strong solution and the existence of the random attractors for the initial boundary value problems to the moist atmospheric equations are proved by using the energy estimations method.The thesis is divided into four chapters.In chapter 1,the initial boundary value problems to moist atmospheric equations are introduced.The concrete expressions of some physical processes,as well as the definition and transformation of random external forcing are given.Then the well-posedness results of the primitive equations for the atmosphere and ocean are introduced.In chapter 2,a new form of the system is obtained by using the correlative transformation of random external forcing,and the basic energy estimations of the initial boundary value problems to the system are established.The existence of the global weak solution is proved by using the Faedo-Galerkin method.TheL~1 stability and almost everywhere stability of global weak solutions are proved as the initial data sequences of the global weak solutions sequences satisfy certain conditions.In chapter 3,theH~1 estimations of the state variables of the system are obtained by using baroclinic decomposition technique and energy estimations method.Then the existence and uniqueness of the global strong solution are proved by using the method of contradiction.The existence of random attractors is also proved as external forcing satisfies certain conditions.In chapter 4,summarize the whole paper and look into the future.