Well-Posedness and Long-Time Dynamics of Geophysical Fluid Flows

This book is intended to cover material for an introductory course in dynamical systems and oceanography, aimed for fourth year undergraduate or first year graduate mathematics students. The material focuses on the three most important aspects of the subject: namely (i) theory, which is to say the questions of existence, uniqueness, and continuous dependence on given data or parameters (ii) phenomenology, meaning the study of properties of solutions that we examine and (iii) applications, by which we mean that we will make an attempt to exercise good scientific taste in choosing the topics in this text, often based on physical or geometrical applications. The purpose of this book is to review the elements of the geodesic transport theory, discuss aspects of its numerical implementation, and present the results from recent applications to problems of geophysical interest.