Pseudospectral and spectral bounds for the Oseen vortices operator

TL;DR

This paper proves spectral and pseudospectral bounds for the linearized Navier-Stokes operator around Oseen vortices, advancing understanding of vortex stability in fluid dynamics.

Contribution

It resolves Gallay's conjecture by establishing spectral and pseudospectral bounds for the linearized operator in two-dimensional fluid flow.

Findings

Proves spectral lower bounds for the linearized operator.

Establishes pseudospectral bounds confirming stability properties.

Advances theoretical understanding of vortex stability in fluid dynamics.

Abstract

In this paper, we solve Gallay's conjecture on the spectral lower bound and pseudospecrtal bound for the linearized operator of the Navier-Stokes equation in $R^2$ around rapidly rotating Oseen vortices.