The Three-Dimensional Navier-Stokes Equations

Part I. Weak and Strong Solutions:
1. Function spaces
2. The Helmholtz–Weyl decomposition
3. Weak formulation
4. Existence of weak solutions
5. The pressure
6. Existence of strong solutions
7. Regularity of strong solutions
8. Epochs of regularity and Serrin's condition
9. Robustness of regularity
10. Local existence and uniqueness in H1/2
11. Local existence and uniqueness in L3
Part II. Local and Partial Regularity:
12. Vorticity
13. The Serrin condition for local regularity
14. The local energy inequality
15. Partial regularity I – dimB(S) ≤ 5/3
16. Partial regularity II – dimH(S) ≤ 1
17. Lagrangian trajectories
A. Functional analysis: miscellaneous results
B. Calderón–Zygmund Theory
C. Elliptic equations
D. Estimates for the heat equation
E. A measurable-selection theorem
Solutions to exercises
References
Index.