Infinite-dimensional dynamical systems in atmospheric and oceanic science / Boling Guo, Daiwen Huang.

Format:

Book

Author/Creator:

Guo, Boling, author.

Huang, Daiwen, author.

Language:

English

Subjects (All):

Marine sciences.

Dynamic meteorology.

Atmospheric circulation.

Physical Description:

1 online resource (329 p.)

Place of Publication:

Singapore ; Hangzhou, China : World Scientific : Zhejiang Science and Technology Publishing House, 2014.

Language Note:

English

Summary:

The book provides some recent works in the study of some infinite-dimensional dynamical systems in atmospheric and oceanic science. It devotes itself to considering some infinite-dimensional dynamical systems in atmospheric and oceanic science, especially in geophysical fluid dynamics. The subject on geophysical fluid dynamics mainly tends to focus on the dynamics of large-scale phenomena in the atmosphere and the oceans. One of the important contents in the dynamics is to study the infinite-dimensional dynamical systems of the atmospheric and oceanic dynamics. The results in the study of some

Contents:

Preface; Contents; 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 Coordinate 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 Coordinate Frame

1.5 Equations of the Atmosphere and the Oceans in Local Rectangular Coordinate Frame under -Plane Approximation1.6 Equations of the Atmosphere and the Oceans under Satification 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 Equation2.3 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; 2.4.2.1 The Surface Quasi-Geostrophic Equation; 2.4.2.2 Dissipative 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 Atmosphere

3.1.2.1 Some Function Spaces3.1.2.2 Some Functionals and the Properties of Their Corresponding Operators; 3.1.2.3 Weak Formulation of Problem IBVP; 3.1.2.4 The Proof of the Global Existence of Weak Solutions; 3.1.2 The Global Existence of Global Weak Solutions of Problem IBVP; 3.1.3 Trajectory and Global Attractors for the Moist Atmospheric Equations; 3.1.3.1 Some Preliminaries about the Trajectory Attractors; 3.1.3.2 Existence of Trajectory and Global Attractors; 3.2 Long-Time Behavior of the Strong Solutions of the Primitive Equations of the Large-Scale Moist Atmosphere

3.2.1 The Primitive Equations of the Large-Scale Moist Atmosphere3.2.2 Main Results; 3.2.3 Uniform Estimates of Local Strong Solutions in Time; 3.2.3.1 Local Existence of the Strong Solutions; 3.2.3.2 A Prior Estimates of Local Strong Solutions; 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; 3.3.2 The Global Well-Posedness of IBVP; 3.3.2.1 The Global Existence of the Weakly Strong Solutions

3.3.2.2 The Uniqueness of Weakly Strong Solution

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

981-4590-38-X