Mathematical geophysics. An introduction to rotating fluids and the Navier–Stokes equations / Математическая геофизика. Введение в движение жидкостей и уравнение Навье-Стокса

This book is divided into four parts. The introduction (Part I) provides the physical background of the geophysical models that are analyzed in this book from a mathematical viewpoint.
Part II is devoted to a self-contained proof of the existence of weak (or strong) solutions to the incompressible Navier–Stokes equations.

Part III deals with the rapidly rotating Navier–Stokes equations, first in the whole space, where dispersion effects are considered. Then the case where the domain has periodic boundary conditions is considered, and finally rotating Navier–Stokes equations between two plates are studied, both in the case of horizontal coordinates in R2 and periodic.
In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed.

The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.