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.
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Description
1. Introduction 2. Linear and nonlinear mechanisms affecting the threshold 3. Key ideas and sketch of the proof 4. Resolvent estimates with Navier-slip boundary condition 5. $L^p$ estimate of the solutions for the homogeneous OS 6. Resolvent estimates via the Neumann boundary data 7. Resolvent estimates when $V=y$ 8. Space-time estimates of the linearized equation 9. Resolvent estimates for the simplified linearized NS system 10. Resolvent estimates for the full linearized NS system 11. Nonlinear interactions 12. Energy estimates for zero mode 13. Energy estimates for nonzero modes:semi-linear part 14. Energy estimates for nonzero modes:quasi-linear part 15. Global stability and long-time behavior