For ideal fluids, Eulerian and Lagrangian instabilities are equivalent

Geometric and Functional Analysis

Volumn 14, Issue 5, 2004, Pages 1044-1062

  Preston, S C ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10144222397     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-004-0482-7     Document Type: Article

References (11)

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2. [AK] V.I. ARNOLD, B.A. KHESIN, Topological Methods in Hydrodynamics. Springer-Verlag, New York, 1998.
3. [BLR] D. BAO, J. LAFONTAINE, T. RATIU, On a nonlinear equation related to the geometry of the diffeomorphism group, Pacific J. Math. 158:2 (1993), 223-242.
4. [C] M.P. DO CARMO, Riemannian Geometry, Birkhäuser, Boston, 1993.
5. [EM] D.G. EBIN, J. MARSDEN, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163.
6. [FV] S. FRIEDLANDER, M.M. VISHIK, Instability criteria for steady flows of a perfect fluid, Chaos 2:3 (1992), 455-460.
7. [MV] F. MAÑOSAS, J. VILLADELPRAT, Area-preserving normalizations for centers of planar Hamiltonian systems, J. Differential Equations 179 (2002), 625-646.
8. [Mi] G.K. MISIOŁEK, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms, Indiana Univ. Math. J. 42:1 (1993), 215-235.
9. [O] W. ORR, The stability or instability of the steady motion of a perfect fluid and of a viscous fluid, part I: A perfect fluid, Proc. Roy. Irish Acad. 27 (1907), 9-68.
10. [P] S.C. PRESTON, Eulerian and Lagrangian stability of fluid motions, PhD Thesis, SUNY Stony Brook, 2002.
11. [R] P. ROUCHON, The Jacobi equation, Riemannian curvature and the motion of a perfect incompressible fluid, European J. Mech. B Fluids 11:3 (1992), 317-336.