Applied Analysis of the Navier-Stokes Equations

This book is an introductory physical and mathematical presentation of the Navier–Stokes equations.

Charles R. Doering (Author), J. D. Gibbon (Author)

9780521445689, Cambridge University Press

Paperback, published 28 April 1995

232 pages, 23 b/w illus. 50 exercises
22.7 x 15.1 x 2 cm, 0.382 kg

'The clear structuring of the scientific content is to be appreciated … The exercises at the end of each chapter are well selected … Hopefully the book will see many editions.' P. Kahlig, Meteorology and Atmospheric Physics

The Navier–Stokes equations are a set of nonlinear partial differential equations comprising the fundamental dynamical description of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier–Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. Intended for graduate students and researchers in applied mathematics and theoretical physics, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses.

1. The equations of motion
2. Dimensionless parameters and stability
3. Turbulence
4. Degrees of freedom, dynamical systems and attractors
5. On the existence, uniqueness and regularity of solutions
6. Ladder results for the Navier–Stokes equations
7. Regularity and length scales for the 2-d and 3-d Navier–Stokes equations
8. Exponential decay of the Fourier power spectrum
9. The attractor dimension for the Navier–Stokes equations
10. Energy dissipation rate estimates for boundary-driven flows.

Subject Areas: Differential calculus & equations [PBKJ]