@inproceedings{19d2f2ef577a47759baaf100acb22e04,

title = "The ORR mechanism: Stability/instability of the Couette flow for the 2D Euler dynamic",

abstract = "We review our works on the nonlinear asymptotic stability and instability of the Couette flow for the 2D incompressible Euler dynamic. In the fits part of the work we prove that perturbations to the Couette flow which are small in Gevrey spaces Gs of class 1/s with s > 1/2 converge strongly in L2 to a shear flow which is close to the Couette flow. Moreover in a well chosen coordinate system, the solution converges in the same Gevrey space to some limit profile. In a later work, we proved the existence of small perturbations in Gs with s < 1/2 such that the solution becomes large in Sobolev regularity and hence yields instability. In this note we discuss the most important physical and mathematical aspects of these two results and the key ideas of the proofs.",

author = "Jacob Bedrossian and Yu Deng and Nader Masmoudi",

note = "Publisher Copyright: {\textcopyright} Proceedings of the International Congress of Mathematicians, ICM 2018. All rights reserved.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",

year = "2018",

language = "English (US)",

series = "Proceedings of the International Congress of Mathematicians, ICM 2018",

publisher = "World Scientific Publishing Co. Pte Ltd",

pages = "2155--2187",

editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",

booktitle = "Invited Lectures",

}