On The Navier-Stokes Equation Of Vorticity Type With Neumann Boundary Conditions

In the paper,we consider the Navier-Stokes equation of vorticity type in a bounded smooth domainΩof R~2,with Neumann bourdary condition.We establish the existence,uniqueness of the weak solution by Galerkin method.After we discuss some problems about the equation itself,we study the convergence of the solution.This thesis is divided into five chapters.In the first chapter,we give the introduction to the problem and the according conclusion.In the second chapter, we introduce notations,formulas and several results that will be used in the following proofs.In the third chapter,we study the Navier-Stokes equation of vorticity type with Neumann bourdary condition.In the fourth chapter,we discuss some problems about the equation itself and the convergence of the equation.At last We draw a conclusion and give some opinions about the future work.