4. THE STOKES OPERATOR

Chapters in this book

1. Frontmatter i
2. CONTENTS v
3. INTRODUCTION vii
4. 1. NOTATION AND PRELIMINARY MATERIAL 1
5. 2. THE STOKES EQUATIONS. EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS 11
6. 3. REGULARITY OF SOLUTIONS OF THE STOKES EQUATIONS 14
7. 4. THE STOKES OPERATOR 31
8. 5. THE NAVIER-STOKES EQUATIONS 45
9. 6. INEQUALITIES FOR THE NONLINEAR TERM 48
10. 7. STATIONARY SOLUTIONS TO THE NAVIER-STOKES EQUATIONS 57
11. 8. WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS 63
12. 9. STRONG SOLUTIONS 74
13. 10. FURTHER RESULTS CONCERNING WEAK AND STRONG SOLUTIONS 83
14. 11. VANISHING VISCOSITY LIMITS 99
15. 12. ANALYTICITY AND BACKWARD UNIQUENESS 104
16. 13. EXPONENTIAL DECAY OF VOLUME ELEMENTS 110
17. 14. GLOBAL LYAPUNOV EXPONENTS. HAUSDORFF AND FRACTAL DIMENSION OF THE UNIVERSAL ATTRACTOR 133
18. 15. INERTIAL MANIFOLDS 154
19. BIBLIOGRAPHY 185
20. INDEX 189