Navier-Stokes Equations and Nonlinear Functional Analysis

Preface to the second edition; Introduction; Part I. Questions Related to the Existence, Uniqueness and Regularity of Solutions: 1. Representation of a Flow: the Navier-Stokes Equations; 2. Functional Setting of the Equations; 3. Existence and Uniqueness Theorems (Mostly Classical Results); 4. New a priori Estimates and Applications; 5. Regularity and Fractional Dimension; 6. Successive Regularity and Compatibility Conditions at t=0 (Bounded Case); 7. Analyticity in Time; 8. Lagrangian Representation of the Flow; Part II. Questions Related to Stationary Solutions and Functional Invariant Sets (Attractors): 9. The Couette-Taylor Experiment; 10. Stationary Solutions of the Navier-Stokes Equations; 11. The Squeezing Property; 12. Hausdorff Dimension of an Attractor; Part III. Questions Related to the Numerical Approximation: 13. Finite Time Approximation; 14. Long Time Approximation of the Navier-Stokes Equations; Appendix. Inertial Manifolds and Navier-Stokes Equations; Comments and Bibliography; Comments and Bibliography; Update for the Second Edition; References.