Memoirs of the American Mathematical Society 2014; 127 pp; softcover Volume: 228 ISBN10: 0821891332 ISBN13: 9780821891339 List Price: US$79 Individual Members: US$47.40 Institutional Members: US$63.20 Order Code: MEMO/228/1073
 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  Introduction
 Formulation and main results
 Linearized problem
 Existence of global weak solutions
 Uniqueness of weak solutions
 Nonlinear stability
 Smoothness of weak solutions
 Some extensions of the theory
 Appendix A. Toolbox
 Bibliography
