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Book Information

Author(s): V. I. Arnold and B. A. Khesin
Title: Topological methods in hydrodynamics
Additional book information: Springer, New York, 1998, xv + 374 pp., $59.95, ISBN 0-387-94947-X

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9.: M.H. FREEDMAN AND Z.-X., HE, Divergence-free fields: energy and asymptotic crossing number, Annals of Math., 134, (1991), no. 1, 189-229. MR 93a:58040
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11.: D.D. HOLM, J.E. MARSDEN, AND T.S. RATIU, Euler-Poincaré equations and semidirect products with applications to continuum theories, Adv. in Math. 137, (1998), 1-81. MR 99e:58070
12.: D.D. HOLM, J.E MARSDEN, T. RATIU, AND A. WEINSTEIN, Nonlinear stability of fluid and plasma equilibria, Phys. Rep., 123, (1985), 1-116. MR 86i:76027
13.: J.E. MARSDEN, A group theoretic approach to the equations of plasma physics, Canad. Math. Bull., 25, (1982), no. 2, 129-142. MR 83h:58044
14.: J.E. MARSDEN AND T.S. RATIU, Introduction to Mechanics and Symmetry, Springer-Verlag, Second Edition, 1999. MR 95i:58073
15.: J.E. MARSDEN, T.S. RATIU, AND S. SHKOLLER, A nonlinear analysis of the averaged Euler equations and a new diffeomorphism group, Geom. Funct. Anal., to appear.
16.: MARSDEN, J.E., T. RATIU, AND A. WEINSTEIN, Semidirect products and reduction in mechanics, Trans. Am. Math. Soc., 281, (1984), 147-177. MR 84k:58081
17.: J.E. MARSDEN AND J. SCHEURLE, The reduced Euler-Lagrange equations, Dynamics and control of mechanical systems (Waterloo, ON, 1992), 139-164, Fields Inst. Commun., 1, Amer. Math. Soc., Providence, RI, 1993. MR 95a:58041
18.: MARSDEN, J.E. AND A. WEINSTEIN, Coadjoint orbits, vortices and Clebsch variables for incompressible fluids, Physica D, 7, (1983), 305-323. MR 85g:58039
19.: MARSDEN, J.E. AND A. WEINSTEIN, The Hamiltonian structure of the Maxwell-Vlasov equations, Phys. D, 4 (1982), no. 3, 394-406. MR 84b:82037
20.: G. MISIOEK, A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys., 24, (1998), 203-208. MR 99d:58018
21.: S. SHKOLLER, Geometry and curvature of diffeomorphism groups with metric and mean hydrodynamics, J. Funct. Anal., 160, (1998), 337-365. CMP 99:06
22.: S. SHKOLLER, The geometry and analysis of non-Newtonian fluids and vortex methods, (1999), E-print math.AP/9908109.
23.: A.I. SHNIRELMAN, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sb. (N.S.), 128(170), (1985), 82-109, 144, MR 87d:58034; Attainable diffeomorphisms, Geom. Funct. Anal., 3, (1993), 279-294, MR 94f:58021; Generalized fluid flows, their approximation and applications, Geom. Funct. Anal., 4, (1994), 586-620. MR 95j:58041

Reviewer(s):
Steve Shkoller
Affiliation: University of California, Davis
Email: shkoller@math.ucdavis.edu

MSC (2000): Primary 22-XX, 35-XX, 53-XX, 58-XX, 76Bxx, 76Exx
DOI: 10.1090/S0273-0979-99-00855-1
PII: S 0273-0979(99)00855-1
Posted: December 21, 1999
Copyright of article: Copyright 2000, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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