Applied Analysis of the Navier-Stokes Equations

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.

• Mathematically rigorous, yet accessible to physicists, engineers, and applied mathematicians
• Exercises and references included, suitable as textbook for introductory course in mathematical fluid dynamics
• Includes new and recent results, bringing the reader to the forefront of research in the field