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

Jacob Bedrossian, Yu Deng, Nader Masmoudi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages2155-2187
Number of pages33
ISBN (Electronic)9789813272927
StatePublished - Jan 1 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume3

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
CountryBrazil
CityRio de Janeiro
Period8/1/188/9/18

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Bedrossian, J., Deng, Y., & Masmoudi, N. (2018). The ORR mechanism: Stability/instability of the Couette flow for the 2D Euler dynamic. In B. Sirakov, P. N. de Souza, & M. Viana (Eds.), Invited Lectures (pp. 2155-2187). (Proceedings of the International Congress of Mathematicians, ICM 2018; Vol. 3). World Scientific Publishing Co. Pte Ltd.