Instability of 2D Couette Flow in Low Regularity Spaces
Time: 2017-12-25
Published By: He Liu
Speaker(s): Yu Deng (New York University)
Time: 14:00-15:00 December 26, 2017
Venue: Room 78201, Jingchunyuan 78, BICMR
In 2013, Bedrossian and Masmoudi proved the stability and asymptotic stability of the Couette flow on T*R for small perturbations in Gevrey class G^(2-). Here, a natural question is whether this high regularity requirement can be relaxed. In this talk, I will present recent work joint with Nader Masmoudi that establishes the optimality of this Gevrey exponent, by proving instability of the Couette flow for small perturbations in any Gevrey class G^(2+). The main ingredients in the proof are: a detailed study of the "toy model" introduced in the work of Bedrossian-Masmoudi, carefully selected perturbations and higher order perturbations, and a combination of physical space and Fourier space techniques.
