The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain

TL;DR

This paper extends the inviscid limit results of Navier-Stokes equations with analytic data from half-spaces to exterior circular domains, overcoming key mathematical challenges using boundary-focused analyticity techniques.

Contribution

It proves the inviscid limit for a broader class of initial data on exterior domains, filling a gap in the mathematical understanding of boundary layer behavior.

Findings

Established inviscid limit for analytic data on exterior domains.

Developed boundary-focused analyticity propagation methods.

Resolved fundamental difficulties related to linear semigroup contractivity.

Abstract

In their classical work [20], Caflisch and Sammartino established the inviscid limit and boundary layer expansions of vanishing viscosity solutions to the incompressible Navier-Stokes equations for analytic data on a half-space. It was then subsequently announced in their Comptes rendus article [4] that the results can be extended to include analytic data on an exterior circular domain, however the proof appears missing in the literature. The extension to an exterior domain faces a fundamental difficulty that the corresponding linear semigroup may not be contractive in analytic spaces as was the case on the half-space [19]. In this paper, we resolve this open problem for a much larger class of initial data. The resolution is due to the fact that it suffices to propagate solutions that are analytic only near the boundary, following the framework developed in the recent works that involve the boundary vorticity formulation, the analyticity estimates on the Green function, the adapted geodesic coordinates near a boundary, and the Sobolev-analytic iterative scheme.