Steady Prandtl Layers over a Moving Boundary: Non-Shear Euler flows

In this article we establish the validity of Prandtl layer expansions around Euler flows which are not shear. The presence of non-shear flows at the leading order creates a singularity of $o(\frac{1}{\sqrt{\epsilon}})$. A new $y$-weighted positivity estimate is developed to control this leading-order growth at the far field.