  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.
