This planet contains so much water that perhaps it should have been better named Oceania. It is the only known body in the solar system that is surrounded by water filled with unique geologic structures and teeming with a staggering assortment of marine life. Some of the strangest creatures on Earth, whose ancestors go back several hundred million years, live on the deep ocean floor.

The formation and evolution of the Earth and planets depend on transfer of mass and energy. Magma and fluid are integral parts of the transport processes that govern the mass and energy transfer. Mass transport property data are central to describe those processes. Mass transport is accomplished by transfer of fluids and magma and typically takes place at high temperature and pressure. Mass transport typically occurs along temperature and pressure gradients, which means that energy transport also associates with mass transport, although in this book, energy transfer is not explicitly discussed.

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.

Various branches of physics and earth sciences have been studied from the  point of view of mathematical morphology and its applications, but for the first time a whole book is devoted to a morphological approach to structural geology. In this sense, it fits in with a long tradition since the two founders of mathematical morphology were both mining engineers.