Synopses & Reviews
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Synopsis
This book describes the general approach to hydrodynamics with its applications to such problems as hydrodynamical stability and fast kinematic dynamo problem, helicity and asymptotic Hopf invariant, to the topology of the stationary solutions of the Euler equations and to integral invariants of ideal fluid hydrodynamics and magnet-hydrodynamics.
Synopsis
The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.
Description
Includes bibliographical references (p. [345]-369) and index.
Table of Contents
Group and Hamiltonian Structures of Fluid Dynamics.- Topology of Steady Fluid Flows.- Topological Properties of Magnetic and Vorticity Fields.- Differential Geometry of Diffeomorphism Groups.- Kinematic Fast Dynamo Problems.- Dynamical Systems with Hydrodynamical Background.- References.- Index.