eBook ISBN:  9781470414856 
Product Code:  MEMO/228/1073.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $47.40 
eBook ISBN:  9781470414856 
Product Code:  MEMO/228/1073.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $47.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 228; 2014; 127 ppMSC: Primary 35; 76
A stationary solution of the rotating NavierStokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating NavierStokesBoussinesq 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 globalintime 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

Chapters

Acknowledgments

1. Introduction

2. Formulation and Main Results

3. Linearized Problem

4. Existence of Global Weak Solutions

5. Uniqueness of Weak Solutions

6. Nonlinear Stability

7. Smoothness of Weak Solutions

8. Some Extensions of the Theory

A. Toolbox


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A stationary solution of the rotating NavierStokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating NavierStokesBoussinesq 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 globalintime 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.

Chapters

Acknowledgments

1. Introduction

2. Formulation and Main Results

3. Linearized Problem

4. Existence of Global Weak Solutions

5. Uniqueness of Weak Solutions

6. Nonlinear Stability

7. Smoothness of Weak Solutions

8. Some Extensions of the Theory

A. Toolbox