Handbook of mathematical fluid dynamics (Elsevier, 2002)
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids
Preface. -- Statistical Hydrodynamics (R. Robert). -- Topics on Dydrodynamics and Volume Preserving Maps (Y. Brenier. -- Weak Solution of Incompressible Euler Equations (A. Shnirelman). -- Near Identity Transformations for the Navier-Stokes Equations (P. Constantin). -- Planar Navier-Stokes Equations Vortificity Approach (M. Ben-Artzi). -- Attractors of Navier-Stokes Equations (A. Babin). -- Stability and Instability in Viscous Fluids (M. Renardy, Y. Renardy). -- Localized Instabilities in Fluids (S. Friedlander, A. Lipton-Lifshitz). -- Dynamo Theory (A.D. Gilbert). -- Water-waves as a Spatial Dynamical System (F. Dias, A. Looss). -- Solving the Einstein Equations by Lipschitz Continuous Metrics: Shock Waves in General Relativity (J. Groah, J. Smoller, B. Temple)
Includes bibliographical references and indexes