Bulletin of the American Mathematical Society

Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid

David G. Ebin and Jerrold E. Marsden

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 75, Number 5 (1969), 962-967.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183530815

Mathematical Reviews number (MathSciNet)
MR0246328

Zentralblatt MATH identifier
0183.54502

Citation

Ebin, David G.; Marsden, Jerrold E. Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid. Bull. Amer. Math. Soc. 75 (1969), no. 5, 962--967. https://projecteuclid.org/euclid.bams/1183530815


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References

  • 1. V. Arnol'd, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), 319-361.
  • 2. G. Duff and D. Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. (2) 56 (1952), 128-156.
  • 3. D. Ebin, The manifold of Riemannian metrics, Proc. Sympos. Pure Math., vol. 15, Amer. Math. Soc. Providence, R.I. (to appear). (See also Bull. Amer. Math. Soc. 74 (1968), 1001-1003.)
  • 4. T. Kato, On classical solutions of the two dimensional non-stationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188-200.
  • 5. J. Leslie, On a differential structure for the group of diffeomorphisms, Topology 6 (1967), 263-271.
  • 6. J. Marsden and R. Abraham, Hamiltonian mechanics on Lie groups and hydrodynamics, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc. Providence, R.I. (to appear).
  • 7. J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294.
  • 8. H. Omori, On the group of diffeomorphisms on a compact manifold, Proc. Sympos. Pure Math., vol. 15, Amer. Math. Soc. Providence, R.I. (to appear).
  • 9. J. Robbin, On the existence theorem for differential equations, Proc Amer. Math. Soc 19 (1968), 1005-1006.
  • 10. S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964), 382-396.