Topological methods in hydrodynamics /
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 ide...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
New York :
Springer,
1998
New York : c1998 New York : 1998 |
| Series: | Applied mathematical sciences (Springer-Verlag New York Inc.) ;
v. 125 Applied mathematical sciences (Springer-Verlag New York Inc.) v. 125 |
| Subjects: |
| Summary: | 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 Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry "Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems, and differential geometry."--BOOK JACKET The book is accessible to graduate students as well as to pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems, and differential geometry |
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| Item Description: | This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |
| Physical Description: | xv, 374 p. : ill. ; 24 cm xv, 374 pages : illustrations ; 24 cm |
| Bibliography: | Includes bibliographical references (p. [345]-368) and index Includes bibliographical references and index |
| ISBN: | 038794947X (hardcover : alk. paper) 038794947X 9780387949475 (hardcover : alk. paper) 9780387949475 |