On A Nonlinear Model For The Antarctic Circumpolar Current

In this paper,we study the existence and uniqueness of solutions of a model for the flow of the Antarctic Circumpolar Current.This paper is divided into four chapters.In chapter 1,we briefly introduce the historical background,research status of circulation motion models,and expound the main result of this paper.By analyzing the physical background,we reduce for flows with no azimuthal variations to a two-point boundary-value problem for a second-order ordinary differential equation and determine the corresponding boundary conditions.In chapter 2,we obtain some radially symmetric results.When satisfies the Osgood condition,we prove that second-order ordinary differential equation have a unique solution,by using the Banach contraction mapping principle and Schauder fixed point theorem.As the special case,we can also obtain the uniqueness of the radially symmetric solution for the Lipschitz case.In chapter 3,we consider the existence of the general solution to circulation models.By some functional-analytic techniques,we prove that,in the Lipschitz case,this problem has only radially symmetric solution,which means that the radially solution we find in chapter 2 is the unique solution to circulation motion models.In chapter 4,we conclude the main content of the whole paper and put forward some problems that can be further considered.