The N-Vortex Problem
This book is an introduction to current research on the N-vortex problem of fluid mechanics in the spirit of several works on N-body problems from ce lestial mechanics, as for example Pollard (1966), Szebehely (1967), or Meyer and Hall (1992). Despite the fact that the field has progressed rapidly in the last 20 years, no book covers this topic, particularly its more recent de velopments, in a thorough way. While Saffman's Vortex Dynamics (1992) covers the general theory from a classical point of view, and Marchioro and Pulvirenti's Mathematical Theory of Incompressible Nonviscous Fluids (1994), Doering and Gibbon's Applied Analysis of the Navier-Stokes Equa tions (1995), and Majda and Bertozzi's Vorticity and Incompressible Fluid Flow (2001) cover much of the relevant mathematical background, none of these discusses the more recent literature on integrable and nonintegrable point vortex motion in any depth. Chorin's Vorticity and Turbulence (1996) focuses on aspects of vorticity dynamics that are most relevant toward an understanding of turbulence, while Arnold and Khesin's Topological Meth ods in Hydrodynamics (1998) lays the groundwork for a geometrical and topological study of the Euler equations. Ottino's The Kinematics of Mix ing: Stretching, Chaos, and Transport (1989) is an introductory textbook on the use of dynamical systems techniques in the study of fluid mixing, while Wiggins' Chaotic Transport in Dynamical Systems (1992) describes techniques that are of general use, without focusing specifically on vortex motion.