# The Vanishing viscosity limit for some symmetric flows

## TL;DR

This paper analyzes the boundary layer behavior and convergence of symmetric flows, specifically plane-parallel and pipe flows, as viscosity approaches zero, by constructing explicit correctors and studying vorticity production.

## Contribution

It introduces explicit boundary layer correctors for symmetric flows and proves optimal convergence rates in the vanishing viscosity limit, extending previous results.

## Key findings

- Established convergence of Navier-Stokes to Euler solutions with optimal rates
- Constructed explicit boundary layer correctors for symmetric flows
- Analyzed vorticity production on the boundary in the vanishing viscosity limit

## Abstract

The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, which approximate the difference between the Navier-Stokes and the Euler solutions. Using properties of these correctors, we establish convergence of the Navier-Stokes solution to the Euler solution as viscosity vanishes with optimal rates of convergence. In addition, we investigate vorticity production on the boundary in the limit of vanishing viscosity. Our work significantly extends prior work in the literature.