Pseudospectrum for Oseen vortices operators

TL;DR

This paper provides resolvent estimates for the linearized Navier-Stokes operator around Oseen vortices in two dimensions, especially in the regime of rapid rotation, enhancing understanding of vortex stability.

Contribution

It introduces new resolvent estimates for the linearized operator around Oseen vortices in the fast rotating limit, advancing the analysis of vortex stability.

Findings

Resolved the behavior of the linearized operator as rotation speed increases

Provided bounds on the resolvent operator in the fast rotation limit

Enhanced theoretical understanding of vortex stability in fluid dynamics

Abstract

In this paper, we give resolvent estimates for the linearized operator of the Navier-Stokes equation in $\R^2$ around the Oseen vortices, in the fast rotating limit $\alpha\to+\infty$.