Handbook of Mathematical Fluid Dynamics
S. Friedlander, D. Serre
Gulf Professional Publishing, Mar 27, 2003 - Science - 626 pages
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.
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Chapter 3 Weak Solutions of Incompressible Euler Equations
Chapter 4 Near Identity Transformations for the NavierStokes Equations
Chapter 6 Attractors of NavierStokes Equations
Chapter 7 Stability and Instability in Viscous Fluids
Chapter 8 Localized Instabilities in Fluids
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2D NS system alpha effect Anal approximation assume Astrophys asymptotic attractor Babin bifurcation boundary conditions bounded components conservation consider constant convection corresponding defined denote density derivatives Differential Equations diffusion dimension domain dynamo action dynamo theory eigenvalues Einstein equations energy equilibrium essential spectrum estimate Euler equations example existence exponential fast dynamo finite finite-dimensional Fluid Dynam fluid flow Fluid Mech FRW metric function Gaussian normal Gaussian normal coordinates given global attractor growth rate homoclinic hydrodynamic incompressible initial data instability integral invariant layer linear Lipschitz continuous magnetic field maps Math measure modes Navier–Stokes equations nonlinear obtain operator parameter perturbation Phys problem proof Renardy rotating satisfies scalar scale Section semigroup shock surface shock wave smooth solitary waves space spectrum stability symmetry Temam tensor theorem theory three-dimensional transformation turbulent two-dimensional vector field velocity field viscosity Vishik vortex vorticity weak solution zero