  Considering the boundary layer problem in the case of two-dimensional flow
past a wedge with the wedge angle $\varphi=\pi\frac{2m}{m+1}$, Oleinik and
Samokhin obtained the local well-posedness results for $m \geq 1$. In this
paper, we establish the existence and uniqueness of classical solutions to the
Prandtl systems for arbitrary $m>0$, which solves the steady case in Open
problem 6 proposed by Oleinik and Samokhin. Our proof is based on the maximum
principle technique at the Crocco coordinates and the most important
observation that when the fluid approaches a sharp point, it seems the
self-similar solutions. Then we obtain the existence and uniqueness of the
solution with the help of the self-similar solutions by the Line Method.
Furthermore, we similarly establish the well-posedness results of
three-dimensional flow past a cone.
