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

## TL;DR

This paper proves the validity of Prandtl layer expansions around non-shear Euler flows, introducing a new weighted positivity estimate to handle singularities caused by non-shear conditions.

## Contribution

It establishes the validity of Prandtl layer expansions for non-shear Euler flows and develops a novel weighted positivity estimate to control singularities.

## Key findings

- Validated Prandtl layer expansions for non-shear flows
- Developed a new y-weighted positivity estimate
- Controlled singularity growth at the far field

## Abstract

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.