The Existence Of Solution For The 2D Navier-Stokes Equations With Friction Boundary In Exterior Domains

Navier-Stokes equation is a kind of equation of motion which describes the con-servation of uid motion among hydromechanics,it has some physical meanings and canexplain kinds of physical phenomena in our life,such as the airow around the wing of theaircraft,the design of aircraft,the ow of liquid in pipeline.The article studies the equa-tion in view of math,introduce existence of the solution of linear and nonlinear Stokesequation in detail.Only the solution exists,we can move forward a single step to studythe situation of viscosity,can further expore.Most reseachers consider the theory of the N-S equation with dirichlet boundaryin unbounded domain .In bound domain,we often use vorticity to proof the existence ofthe solution.We will take into account properties of solutions of N-S equation with fric-tion boundary with friction boundary.Because we change the domain,the former methoddoesn't apply,so we must change it.The paper make use of potential theory and contrac-tion mapping principle to proof the existence of the solution of N-S equation.In the paper,chapter I introduce the background knowledge of N-S equation as wellas previous reseach results and the main results and arrangement of the article.ChapterII solve Laplace equation in the circular domain and give specific form.Chapter III usepotential theory to proof the existence of the linear Stokes equation .Chapter IV proofthe situation of the nolinear equation.When the solutions of the stationary Navier-Stokesequations exists in exterior domains,we continue to reseach the solutions of the nonsta-tionary Navier-Stokes equations.