Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid
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- by David G. Ebin and Jerrold E. Marsden PDF
- Bull. Amer. Math. Soc. 75 (1969), 962-967
References
- V. Arnold, 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), no. fasc. 1, 319–361 (French). MR 202082, DOI 10.5802/aif.233
- G. F. D. Duff and D. C. Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. (2) 56 (1952), 128–156. MR 48137, DOI 10.2307/1969771
- David G. Ebin, On the space of Riemannian metrics, Bull. Amer. Math. Soc. 74 (1968), 1001–1003. MR 231410, DOI 10.1090/S0002-9904-1968-12115-9
- Tosio Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188–200. MR 211057, DOI 10.1007/BF00251588
- J. A. Leslie, On a differential structure for the group of diffeomorphisms, Topology 6 (1967), 263–271. MR 210147, DOI 10.1016/0040-9383(67)90038-9 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).
- Jürgen Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294. MR 182927, DOI 10.1090/S0002-9947-1965-0182927-5
- Hideki Omori, On the group of diffeomorphisms on a compact manifold, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 167–183. MR 0271983
- Joel W. Robbin, On the existence theorem for differential equations, Proc. Amer. Math. Soc. 19 (1968), 1005–1006. MR 227583, DOI 10.1090/S0002-9939-1968-0227583-0
- S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964), 382–396. MR 165539, DOI 10.2307/1970398
Additional Information
- Journal: Bull. Amer. Math. Soc. 75 (1969), 962-967
- DOI: https://doi.org/10.1090/S0002-9904-1969-12315-3
- MathSciNet review: 0246328