The inviscid limit of Navier-Stokes for analytic data on the half-space

TL;DR

This paper proves the inviscid limit of the Navier-Stokes equations for analytic data in the half-space without constructing boundary layer correctors, using boundary vorticity and Cauchy-Kovalevskaya theorem.

Contribution

It provides a direct proof of the inviscid limit for analytic data, bypassing the need for Prandtl boundary layer expansions.

Findings

Established inviscid limit for general analytic data

Used boundary vorticity formulation and Cauchy-Kovalevskaya theorem

Simplified proof avoiding boundary layer correctors

Abstract

In their classical work Caflisch and Sammartino proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl's boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl's boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.