Navier-Stokes Equations

by Peter Constantin and Ciprian Foias

University of Chicago Press, 1988
Cloth: 978-0-226-11548-1 | Paper: 978-0-226-11549-8 | Electronic: 978-0-226-76432-0
DOI: 10.7208/chicago/9780226764320.001.0001

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ABOUT THIS BOOKAUTHOR BIOGRAPHYTABLE OF CONTENTS

ABOUT THIS BOOK

Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.

AUTHOR BIOGRAPHY

Peter Constantin is professor of mathematics at the University of Chicago. Ciprian Foias is Distinguished Professor in Mathematics at Indiana University.

Introduction

Chapter 1. Notation and Preliminary Material

Chapter 2. The Stokes equations. Existence and Uniqueness of Weak Solutions

Chapter 3. Regularity of Solutions of the Stokes Equations

Chapter 4. The Stokes Operator

Chapter 5. The Navier-Stokes Equations

Chapter 6. Inequalities for the Nonlinear Term

Chapter 7. Stationary solutions to the Navier-Stokes Equations

Chapter 8. Weak Solutions of the Navier-Stokes Equations

Chapter 9. Strong Solutions

Chapter 10. Further Results Concerning Weak and Strong Solutions

Chapter 11. Vanishing Viscosity Limits

Chapter 12. Analyticity and Backward Uniqueness

Chapter 13. Exponential Decay of Volume Elements

Chapter 14. Global Lyapunov Exponents. Hausdorff and Fractal Dimension of the Universal Attractor

Chapter 15. Inertial Manifolds

Bibliography

Index