Boundary Layers Associated With Incompressible Navier-Stokes Equations

In this paper,we study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are permeable,and prove that there exists the first order boundary layer at the outlet.As the viscosity of the fluid,such as water and air,is in general small,the viscous force seems to be ignored while compared with other forces,such as inertia force, gravity and press force.But in 1744,d'Alembert found that if we consider the fluid as no viscosity,the results of the theoretical analysis are different from the experiment.In 1904,Prantle.L introduced the concept of the boundary layer in the fluid flow over a surface on the third International Mathematical Congress.By the singular perturbation, we find the equations of the boundary layer.Then,we study the equations and know that they're well-posed and smooth enough.We say the approximation is suitable in L~∞.