《大气海洋无穷维动力系统(英文版)(精)》由郭柏灵院士主编，郭院士研究无穷维动力系统多年，取得了一些重大研究成果。大气、海洋无穷维动力系统是大气和海洋动力学理论研究的重要内容之一。《大气海洋无穷维动力系统(英文版)(精)》共分五章，主要介绍了该系统中重要的新近研究成果。

1. Nonlinear Equations of the Atmospheric and the Oceanic

 Motions

 1.1 Basic Equations of the Atmospheric and the Oceanic Motions

 1.1.1 Basic Equations of the Atmosphere

 1.1.2 Basic Equations of the Oceans

 1.2 Equations of the Atmosphere and the Oceans in the Sphere

 Coordinate Frame

 1.2.1 Equations of the Atmosphere in the Sphere Coor-

 dinate Frame

 1.2.2 Equations of the Oceans in the Sphere Coordinate

 Frame

 1.3 Equations of the Atmosphere in Atmospheric Pressure

 Coordinate Frame

 1.4 Equations of the Atmosphere in the Topography Coordi-

 nate Frame

 1.5 Equations of the Atmosphere and the Oceans in Local

 Rectangular Coordinate Frame under/%Plane Approxima-

 tion

 1.6 Equations of the Atmosphere and the Oceans under Sati-

 fication Approximation

 1.7 Boundary Conditions

 1.7.1 The Lower Boundary Conditions of the Atmosphere

 1.7.2 The Upper Boundary Conditions of the Atmosphere

 1.7.3 The Boundary Conditions of the Oceans

2. Some Quasi-Geostrophic Models

 2.1 The Barotropic Model and the Two-Dimensional Quasi-

 Geostrophic Equation

 2.1.1 The Barotropic Model

 2.1.2 The Two-Dimensional Quasi-Geostrophic Equation

 2.2 Three-Dimensional Quasi-Geostrophic Equation

 2.3 The Multi-Layer Quasi-Geostrophic Model

 2.4 The Surface Quasi-Geostrophic Equation

 2.4.1 Introduction of Surface Quasi-Geostrophic Equation

 2.4.2 Some Results of Surface Quasi-Geostrophic Equation

3. Well-Posedness and Global Attractors of the Primitive

 Equations

 3.1 Existence of Weak Solutions and Trajectory Attractors of

 the Moist Atmospheric Equations

 3.1.1 Primitive Equations of the Large-Scale Moist At-

 mosphere

 3.1.2 The Global Existence of Global Weak Solutions of

 Problem IBVP

 3.1.3 Trajectory and Global Attractors for the Moist At-

 mospheric Equations

 3.2 Long-Time Behavior of the Strong Solutions of the Primi-

 tire Equations of the Large-Scale Moist Atmosphere . . .

 3.2.1 The Primitive Equations of the Large-Scale Moist

 Atmosphere

 3.2.2 Main Results

 3.2.3 Uniform Estimates of Local Strong Solutions in Time

 3.2.4 Global Existence and Uniqueness of Strong

 Solutions

 3.2.5 Some Preliminaries about the Infinite-Dimensional

 Dynamical System

 3.2.6 The Existence of Global Attractors

 3.3 The Global Well-Posedness of the Primitive Equations . .

 3.3.1 Main Results i

 3.3.2 The Global Well-Posedness of IBVP

 3.3.3 The Global Existence of Smooth Solutions of IBVP

 3.4 Global Well-Posedness of Primitive Equations of the

 Oceans

 3.4.1 The Viscous Primitive Equations of the Large-

 Scale Oceans

 3.4.2 Main Results 1

 3.4.3 The Local Existence of Strong Solutions 1

 3.4.4 The Global Existence and Uniqueness of Strong

 Solutions

4. Random Dynamical Systems of Atmosphere and Ocean

 4.1 Random Attractors of Two-Dimensional Quasi-Geostrophic

 Dynamical System

 4.1.1 Model

 4.1.2 Global Existence and Uniqueness of Solutions

 4.1.3 Preliminaries of Random Attractors

 4.1.4 Existence of Random Attractors

 4.1.5 Stochastic Quasi-Geostrophic Equations on

 Unbounded Domains

 4.2 Global Well-Posedness and Attractors of 3D Stochastic

 Primitive Equations of the Large-Scale Oceans

 4.2.1 Three-Dimensional Stochastic Equations of the

 Large-Scale Oceans

 4.2.2 New Formulation of IBVP

 4.2.3 Existence and A Priori Estimate of Local Solutions

 4.2.4 The Global Well-Posedness of IBVP

 4.2.5 Existence of Random Attractors

 4.3 The Primitive Equations of Large-Scale Oceans with Ran-

 dom Boundary

 4.3.1 Model

 4.3.2 The New Formulation of the Initial-Boundary

 Value Problem (4.3.10)-(4.3.17)

 4.3.3 The Global Well-Posedness of the Primitive Equa-

 tions with Random Boundary

 4.3.4 Existence of Random Attractors

5. Stability and Instability Theory

 5.1 Stability and Instability of Gravity Waves

 5.1.1 Stability and Instability of Internal Gravity Waves

 in Stratified Flows

 5.1.2 Stability of General Internal Gravity Wave

 5.1.3 Stability of General Inertial Internal Gravity Wave

 5.2 Instability of Rossby Waves

 5.2.1 Necessary Conditions of Linear Instability

 5.2.2 Linear Instability of Barotropic Rossby Waves .

 5.2.3 Linear Instability of Baroclinic Rossby Waves .

 5.3 Stability of Rossby Waves

 5.3.1 Stability of Bidimensional Quasi-Geostrophic Flow

 5.3.2 Stability of Saddle-Point-Type Two-Dimensional Quasi-

 Geostrophic Flows

 5.4 Critical Rayleigh Number of Rayleigh-Benard Convection

 5.4.1 Linear Stability

 5.4.2 Nonlinear Stability for Ra<R*a

 5.4.3 Nonlinear Instability for Ra> R*a

References