Transition Threshold for the 3D Couette Flow in a Finite Channel

Qi Chen, Zhejiang University, Hangzhou, People's Republic of China, Dongyi Wei, Peking University, Beijing, People's Republic of China, and Zhifei Zhang, Peking University, Beijing, People's Republic of China.

• 1. Introduction2. Linear and nonlinear mechanisms affecting the threshold3. Key ideas and sketch of the proof4. Resolvent estimates with Navier-slip boundary condition5. $L^p$ estimate of the solutions for the homogeneous OS6. Resolvent estimates via the Neumann boundary data7. Resolvent estimates when $V=y$8. Space-time estimates of the linearized equation9. Resolvent estimates for the simplified linearized NS system10. Resolvent estimates for the full linearized NS system11. Nonlinear interactions12. Energy estimates for zero mode13. Energy estimates for nonzero modes:semi-linear part14. Energy estimates for nonzero modes:quasi-linear part15. Global stability and long-time behavior