Résumé
This comprehensive introduction to the mathematics of incompressible fluid mechanics and its applications is aimed at undergraduate and graduate students across mathematics, physics, engineering, chemistry and the life sciences. It progresses from the very basics to advanced material, with exercises, mini-projects and real-life examples included.This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum - only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.Preface; Introduction; Part I. Inviscid Flow: 1. Flow and transport; 2. Ideal fluid flow; 3. Two-dimensional irrotational flow; Part 2. Viscous Flow: 4. Navier-Stokes flow; 5. Low Reynolds number flow; 6. Bounday layer theory; 7. Navier-Stokes regularity; Appendix; Bibliography; Index.Frank H. Berkshire is currently Principal Teaching Fellow in Dynamics in the Department of Mathematics at Imperial College London, where he has been a member of the Academic Staff since 1970-latterly for twenty-five years as Director of Undergraduate Studies until formal 'retirement' in 2011. He has long-term experience of delivering lecture courses and projects, and has received awards for teaching excellence. He has promoted Mathematics extensively in the UK and overseas, and is co-author with Tom Kibble of the textbook Classical Mechanics (1996 and 2004). His research interests are in theoretical and practical dynamics, with wide application in e.g. waves, vortices, planetary motion, chaos, sport and gambling. Simon J. A. Malham is Associate Professor of Mathematics at Heriot-Watt University. After obtaining his Ph.D. from Imperial College London in 1993, he was a Visiting Assistant Professor at the University of Arizona (1993-6), a temporary lecturer at the University of Nottingham (1996-8) and Imperial (1998-2000), before joining Heriot-Watt as a lecturer in 2000. His research interests include Navier-Stokes regularity, the stability of nonlinear travelling fronts, computational spectral theory, the optimal simulation of stochastic differential equations including Lie group methods, Hopf algebra analysis and almost-exact methods, Grassmannian flows and the representation and integrability of non-commutative local and nonlocal nonlinear partial differential systems. J. Trevor Stuart is Professor Emeritus in the Department of Mathematics at Imperial College London. After obtaining his Ph.D. from Imperial in 1951, he worked at the National Physical Laboratory in the Aerodynamics Division from 1951 to 1966, before joining the Mathematics Department at Imperial in 1966. He retired in 1994. Professor Stuart was a Visiting Professor at MIT in 1956-7 and 1965-6, as well as at Brown University in 1988-9. He became a Fellow of the Royal Society (FRS) in 1974 and was awarded the Otto Laporte Award from the American Physical Society in 1985 as well as the Senior Whitehead Prize from the London Mathematical Society in 1984. He holds honorary Doctor of Science degrees from Brown University and the University of East Anglia.
