Infinite-dimensional Dynamical Systems in Atmospheric and Oceanic Science

1. Nonlinear equations of the atmospheric and the oceanic motions. 1.1. Basic equations of the atmospheric and the oceanic motions. 1.2. Equations of the atmosphere and 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 [beta symbol]-plane approximation. 1.6. Equations of the atmosphere and the oceans under satification approximation. 1.7. Boundary conditions -- 2. Some quasi-geostrophic models. 2.1 The barotropic model and 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 -- 3. Well-posedness and global attractors of the primitive equations. 3.1. Existence of weak solutions and trajectory attractors of the moist atmospheric equations. 3.2. Long-time behavior of the strong solutions of the primitive equations of the large-scale moist atmosphere. 3.3. The global well-posedness of the primitive equations. 3.4. Global well-posedness of primitive equations of the oceans -- 4. Random dynamical systems of atmosphere and ocean. 4.1. Random attractors of two-dimensional quasi-geostrophic dynamical system. 4.2. Global well-posedness and attractors of 3D stochastic primitive equations of the large-scale oceans. 4.3. The primitive equations of large-scale oceans with random boundary -- 5. Stability and instability theory. 5.1 Stability and instability of gravity waves. 5.2. Instability of Rossby waves. 5.3. Stability of Rossby waves. 5.4. Critical Rayleigh number of Rayleigh-Benard convection