The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
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
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.
