Navier-Stokes Equations and Nonlinear Functional Analysis
Navier-Stokes Equations and Nonlinear Functional Analysis
Paperback
This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds.
Product details
December 1996Paperback
9780898713404
155 pages
252 × 173 × 10 mm
0.278kg
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Table of Contents
- 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.
