Nonlinear inviscid damping for a class of monotone shear flows in a finite channel

Abstract

We prove the nonlinear inviscid damping for a class of monotone shear flows in $\mathbb{T}\times [0,1]$ for initial perturbation in Gevrey-$\frac{1}{s}$ class ($1\lt \frac{1}{s}<2$) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.

Authors

Nader Masmoudi

New York University in Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates and Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

Weiren Zhao

New York University in Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates