# Real analytic local well-posedness for the Triple Deck

## TL;DR

This paper establishes local well-posedness for the Triple Deck model, a high-order boundary layer system, by splitting it into coupled equations and exploiting cancellations in a real analytic framework.

## Contribution

It introduces a novel splitting of the Triple Deck system into coupled equations and develops a functional framework to prove well-posedness in real analytic spaces.

## Key findings

- Proves local well-posedness of the Triple Deck model.
- Identifies a crucial cancellation enabling analysis.
- Develops a new analytical framework for boundary layer models.

## Abstract

The Triple Deck model is a classical high order boundary layer model that has been proposed to describe flow regimes where the Prandtl theory is expected to fail. At first sight the model appears to lose two derivatives through the pressure-displacement relation which links pressure to the tangential slip. In order to overcome this, we split the Triple Deck system into two coupled equations: a Prandtl type system on $\mathbb{H}$ and a Benjamin-Ono type equation on $\mathbb{R}$. This splitting enables us to extract a crucial leading order cancellation at the top of the lower deck. We develop a functional framework to subsequently extend this cancellation into the interior of the lower deck, which enables us to prove the local well-posedness of the model in tangentially real analytic spaces.