内容

目次

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