Linear Stability of the 2D Irrotational Circulation Flow around An Elliptical Cylinder

TL;DR

This paper proves a linear inviscid damping result with optimal decay rates for 2D irrotational flow around an elliptical cylinder, showing non-vanishing asymptotic velocity components and altered flow lines.

Contribution

It establishes the linear stability and decay rates of irrotational flow around an elliptical cylinder, revealing new flow behavior at asymptote.

Findings

Optimal decay rates for flow components

Non-vanishing asymptotic velocity components

Flow lines are not elliptical at infinity

Abstract

In this article we prove a linear inviscid damping result with optimal decay rates of the 2D irrotational circulation flow around an elliptical cylinder. In our result, all components of the asymptotic velocity field do not vanish and the asymptotic flow lines are not ellipse any more.