Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
邓 煜 博士, Courant研究所, USA
Inviter:
Title:
Instability of 2D Couette flow in low regularity spaces
Time & Venue:
2017.12.22 16:20-17:20 N913
Abstract:
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.