Global Well-posedness Of The Boundary Layer Equations From Euler-? Equations In Half Plane

In this paper,we mainly study the existence and uniqueness of the global solutions of the boundary layer equations with no-slip boundary conditions for Euler-? equations in the half plane.Near the boundary of the domain,the main enlightenment of this problem is the boundary layer produced by the mismatch between the homogeneous boundary condition u=0 satisfied by the Euler-?equations and the non-penetration boundary condition u·n=0 satisfied by the Euler equations.In the boundary layer equations,in order to overcome the difficulty caused by the loss of a derivative of in the horizontal direction,this paper selects an appropriate analytic function space to investigate the existence and uniqueness of the solution of the boundary layer equations.First,the boundary layer equations of Euler-? equations are obtained by using the formal expansion.In the constructed analytic space the existence and uniqueness of the boundary layer equations are obtained by using the abstract Cauchy-Kovalevskaya theorem.Finally,by solving the global formal solution of the boundary layer equations,it is verified that there is a global unique solution of the boundary layer equations.