The Navier-Stokes equations. A classification of flows and exact solutions.

*(English)*Zbl 1154.76019
London Mathematical Society Lecture Note Series 334. Cambridge: Cambridge University Press (ISBN 0-521-68162-6/pbk). x, 196 p. (2006).

The Navier-Stokes equations were established in the nineteenth century as the system of nonlinear partial differential equations that describe the motion of most commonly occurring fluids in air and water. Since that time scientists are interested in their exact solutions. The book collects a lot of exact solutions to special flow situations. These solutions allow a clear insight into the behaviour of fluids, providing a vehicle for novel mathematical methods and a useful check for computations in fluid dynamics. This book draws together exact solutions from widely differing sources and presents them in a coherent manner, in part giving a classification of solutions via their temporal and geometric constraints. It is a valuable resource for learning and teaching fluid mechanics at senior undergraduate and graduate levels.