On Boundary Regularity Of2D Navier-Stokes Equations

Navier-Stokes equations are a kind of equations which describe the conservation offluid motion among hydromechanics, it can explain kinds of physical phenomena in ourlife, such as the airflow around the wing of the aircraft and the design of aircraft, the flow ofliquid in pipeline.Most articles study the inner regularity of weak solutions of Navier-Stokes equationsin dimension greater than2according to the knowledge of math. There is few papers thatconsider the case of boundary regularity. We use the method of Fourier transform to studythe boundary regularity of nonlinear Navier-Stokes equations in upper half plane. In addi-tion, we also discuss the properties of the solutions in an external domains. As the changesof the domains, we can’t use the original method. So we show the existence of the solutionsin an external domains by the knowledge of curl and the second-order parabolic equations.In this paper, chapter I introduces the background knowledge of Navier-Stokesequations as well as previous research results and the main results and arrangement of thearticle. Chapter II derives the Green tensor for the linear Stokes system in a half-plane bythe method of Fourier transform and shows the point-wise estimates of that tensor. ChapterIII discusses the boundary regularity of nonlinear equations by using Main Theorem andpotential method. Chapter IV discusses the existence of the weak solutions in an exteriordomain.