**Memoirs of the American Mathematical Society**

2014;
127 pp;
Softcover

MSC: Primary 35; 76;

Print ISBN: 978-0-8218-9133-9

Product Code: MEMO/228/1073

List Price: $79.00

AMS Member Price: $47.40

MAA Member Price: $71.10

**Electronic ISBN: 978-1-4704-1485-6
Product Code: MEMO/228/1073.E**

List Price: $79.00

AMS Member Price: $47.40

MAA Member Price: $71.10

# Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids

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*Hajime Koba*

A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.

#### Table of Contents

# Table of Contents

## Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids

- Acknowledgments vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Formulation and Main Results 716 free
- Chapter 3. Linearized Problem 1524
- Chapter 4. Existence of Global Weak Solutions 4756
- Chapter 5. Uniqueness of Weak Solutions 7382
- Chapter 6. Nonlinear Stability 8594
- Chapter 7. Smoothness of Weak Solutions 91100
- Chapter 8. Some Extensions of the Theory 107116
- Appendix A. Toolbox 113122
- Bibliography 125134