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Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
Open accessAbstract
Les théorèmes d’Euler sur les géodésiques du groupe S O ( 3 ) , muni d’une métrique invariante à gauche, sont extendus pour un groupe de Lie arbitraire, en particulier groupe SDiffD des difféomorphismes de D , conservant le volume. Les géodésiques de SDiffD étant écoulement de fluides parfaits, on obtient des critères de stabilité en hydrodynamique non linéaire. On calcule la courbure riemannienne de SDiffD, qui se trouve négative dans la plupart des sections.
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Cited by
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
Holm, D. D., Marsden, J. E., & Ratiu, T. S. (1998) · Advances in Mathematics · doi:10.1006/aima.1998.1721 · Cited by 964
Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism
Öttinger, H. C., & Grmela, M. (1997) · Physical Review E · doi:10.1103/physreve.56.6633 · Cited by 770
Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids
Marsden, J., & Weinstein, A. (1983) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(83)90134-3 · Cited by 481
Statistics on diffeomorphisms via tangent space representations
Vaillant, M., Miller, M. I., Younes, L., & Trouvé, A. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2004.07.023 · Cited by 215
Linear canonical transformations and quantum phase: a unified canonical and algebraic approach
Hakioglu, T. (1999) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/32/22/312 · Cited by 9
Metadata
- Authors
- Arnold, V.
- Venue
- Annales de l'Institut Fourier
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1966
- Volume
- 16
- Issue
- 1
- Pages
- 319-361
- ISSN
- 0373-0956 (ISSN-L)
- 1777-5310
- OpenAlex
- W1994088960
- Cited by
- 1,609
- References
- 0
- FWCI
- 2.75
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Arnold, V. (1966). Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Annales de l'Institut Fourier. https://doi.org/10.5802/aif.233
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