New developments on existence and uniqueness of solutions to some models in atmospheric dynamics

Abstract

This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two- and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instatibility and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.