Remark on a lower bound of perturbations in 2D inviscid shear flow in a periodic box

TL;DR

This paper establishes a lower bound on perturbations in 2D inviscid shear flows within a periodic domain, building on previous stability results and mathematical tools from diffeomorphism groups.

Contribution

It provides a new lower bound for perturbations in 2D inviscid shear flows in a periodic setting, extending prior stability analyses.

Findings

Lower bound of perturbations established

Extension of stability results to periodic domains

Integration of diffeomorphism group techniques

Abstract

Bedrossian and Masmoudi (2015) showed nonlinear stability of 2D inviscid parallel shear flows in the infinite stripe $(\mathbb{R}/2\mathbb{Z})\times\mathbb{R}$. Inspired by their result, combining a diffeomorphism group result by Misio{\l}ek (1993), in this paper we give a lower bound of perturbations in 2D inviscid shear flow in a periodic box.