In this very nice book the authors study a model describing the motion of the ocean in the equatorial zone. For the description of the flow, a viscous Saint Venant model for rotating fluid is used. It takes into account gravity, the Coriolis force and depth variation of the fluid h=H(1+εη) around a mean depth H. The system can be rewritten in a form similar to the Navier-Stokes equations with a singular perturbation of order 1/ε. The first chapter of the book is introductory. The second studies the spectral decomposition of the singular perturbation. The third chapter is devoted to the study of well-posedness of the formal limiting problem as ε goes to 0. In the last chapter the limiting process is justified. The book is well written, nicely structured and very clear. Any researcher in the field would enjoy it. The book could also be appreciated by graduate students interested in the study of rotating fluids.

Reviewer:

pkap