The Three-Dimensional Navier–Stokes Equations : Classical Theory (Hardcover)

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. Calderon?Zygmund Theory; C. Elliptic equations; D. Estimates for the heat equation; E. A measurable-selection theorem; Solutions to exercises; References; Index.