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Applied Analysis of the Navier-Stokes Equations
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The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the fundamental dynamics 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. The goal of the book is to present a mathematically rigorous investigation of the Navier-Stokes equations that is accessible to a broader audience than just the subfields of mathematics to which it has traditionally been restricted. Therefore, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses. This book is appropriate for graduate students in many areas of mathematics, physics, and engineering.
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Table of Contents

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.

Reviews

'The book is written for anyone who strives to understand the inherent difficulties of the nonlinear Navier-Strokes equations ... Hopefully, the book will see many editions.' P. Kahlig, Meteorology and Atmospheric Physics ' ... the authors have done a thoughtful job of expounding ideas that are not close to the hearts of many mathematicians yet are capable of providing new basic and computational understandings.' J. R. Ockendon, Journal of Fluid Mechanics '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

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