The existence and uniqueness of self-similar solutions describing flow in mixing layers

A solution to the stream function equation for a mixing layer is usually sought within a class of self-similar functions. This is explained by the fact that flow in boundary layers is largely determined by the boundary conditions, while being only slightly dependent on the initial conditions. The self-similar functions satisfy a third-order nonlinear equation with three boundary conditions. It is proved that for all boundary value problems, there exists a solution to the above equation.