Nonlinear Instability in Two Dimensional Ideal Fluids: The Case of a Dominant Eigenvalue

Communications in Mathematical Physics

Volumn 243, Issue 2, 2003, Pages 261-273

  Vishik, Misha ^a   Friedlander, Susan ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346365501     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0963-9     Document Type: Article

References (11)

1. [A] Arnold, V.I.: Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, Vol. 60, Berlin-Heidelberg-New York: Springer, 1980
2. [BGS] Bardos, C., Guo, Y., Strauss, W.; Stable and unstable ideal plane flows. To appear
3. [FSV-1] Friedlander, S., Strauss, W., Vishik, M.: Nonlinear instability in an ideal fluid. Ann. Inst. Henri. Poincaré, Analyse Nonlinéaire 14(2), 187-209 (1997)
4. [FSV-2] Friedlander, S., Strauss, W., Vishik, M.: Robustness of instability for the two dimensional Euler equations. SIAM J. Math. Anal. 30(6), 1343-1355 (1999)
5. [G] Grenier, E.: On the nonlinear instability of the Euler and Prandtl equations. Comm. Pure Appl. Math. 53(9), 1067-1091 (2000)
6. [K] Koch, H.: Instability for incompressible and inviscid fluids. In: Partial Differential Equations, Praha, 1998, CRC Res. Notes Math. 406, London: Chapman Hall, 1999, pp. 240-247
7. [L] Lamb, H.: Hydrodynamics. 6th Ed., New York: Dover, 1945
8. [LV] Latushkin, Y., Vishik, M.: Linear stability in an ideal incompressible fluid. Commun. Math. Phys. 233, 439-461 (2003)
9. [R] Lord Rayleigh: On the stability or instability of certain fluid motions. Proc. Lond. Math. Soc. 9, 57-70 (1880)
10. [V] Vishik, M.: Spectrum of small oscillations of an ideal fluid and Lyapunov exponents. J. Math. Pures et. Appl. 75, 531-557 (1996)
11. [Y] Yudovich, V.: On the loss of smoothness of the solutions of the Euler equations and the inherent instability of flows of an ideal fluid. Chaos. 10(3), 705-719 (2001)