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# đź“™ Nonlinear stability of Ekman boundary layers in rotating stratified fluids by Hajime Koba â€” free pdf

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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

## About book:

## About file:

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- Series:
**Memoirs of the American Mathematical Society 1073** - Author:
**Hajime Koba** - Year:
**2014** - Publisher:
**Amer Mathematical Society** - Language:
**English** - ISBN:
**0821891332,978-0-8218-9133-9**

- File size:
**963 043** - Format:
**pdf**

Security code:

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an introÂ duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layer...

Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology, and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dyn...

The book presents a comprehensive overview of the current state-of-the-art in the atmospheric boundary layer (ABL) research. It focuses on experimental ABL research, while most of the books on ABL discuss it from a theoretical or fluid dynamics point of v...

Prandtlâ€™s famous lecture with the title â€śĂśber FlĂĽssigkeitsbewegung bei sehr kleiner Reibungâ€ť was presented on August 12, 1904 at the Third Internationalen Mathematischen Kongress in Heidelberg, Germany. This lecture invented the phrase â€śBoundary Layerâ€ť (G...

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary...

This book is devoted to finite volume methods for hyperbolic systems of conservation laws. The accent is put on the development of tools for analyzing the nonlinear stability of Godunov schemes. Starting from theoretical considerations, the schemes are de...

This volume presents peer-reviewed papers from the NATO Advanced Research Workshop on Atmospheric Boundary Layers held in April 2006. The papers are divided into thematic sessions: nature and theory of turbulent boundary layers; boundary-layer flows: mode...

Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situations-whether in the liquid or gaseous state or both-is introduced and comprehensively covered in this widely adopted text. Fully revised and upd...

Part of the excitement in boundary-layer meteorology is the challenge associated with turbulent flow - one of the unsolved problems in classical physics. The flavor of the challenges and the excitement associated with the study of the atmospheric boundary...

This volume presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. It is an extension of and a supplement to Volume A, Space-group symmetry, in which only basic data for sub-...

Astronomy and Astrophysics were first treated in volume III of the 6th edition of Landolt-BĂ¶rnstein in 1952, then in volumes VI/1 and VI/2 of the New Series, 1965 and 1981/82 respectively. The present volume VI/3 is a further supplementation of volume VI/...

Introduces a new approach to rock mechanics called ``block theory,'' which formalizes procedures for selecting proper shapes and orientations for excavations in hard jointed rock. Applies block theory to rock slopes and underground excavations, and covers...

There are many textbooks for business students that provide a systematic, introductory development of the economics of financial markets. However, there are as yet no introductory textbooks aimed at more easily daunted undergraduate liberal arts students....

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