Mathematical Geophysics - An Introduction to Rotating Fluids and the Navier-Stokes Equations
Making the subtitle more specific, this book provides a transparent introduction to the mathematical analysis of rotating incompressible fluids described by the evolutionary Navier-Stokes equations (NSEs) with dominant Coriolis forces. The authors first discuss physical aspects related to the investigated geophysical model. Then, after recalling necessary facts on function spaces, the theory of weak solutions related to the three-dimensional Navier-Stokes equations is provided. Next, NSEs with significant Coriolis forces are treated in various geometries: in the whole space, in domains with periodic boundary conditions and in domains bounded by two parallel plates. The final part focuses on the boundary layer phenomena related to the investigated systems and to some other relevant problems. This well organized and nicely presented book can be recommended to everybody interested in mathematical issues related to the Navier-Stokes equations and to geophysical fluid mechanics, as well as to the stability theory for dynamical systems described by systems of partial differential equations.