Nonlinear instability in an ideal fluid
Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 2, p. 187-209
@article{AIHPC_1997__14_2_187_0,
     author = {Friedlander, Susan and Strauss, Walter A. and Vishik, Misha},
     title = {Nonlinear instability in an ideal fluid},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {2},
     year = {1997},
     pages = {187-209},
     zbl = {0874.76026},
     mrnumber = {1441392},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1997__14_2_187_0}
}
Friedlander, Susan; Strauss, Walter; Vishik, Misha. Nonlinear instability in an ideal fluid. Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 2, pp. 187-209. http://www.numdam.org/item/AIHPC_1997__14_2_187_0/

[BB] J. Bourguignon and H. Brezis, Remarks on the Euler equation, J. Funct. Anal., Vol. 15, 1974, 4, pp. 341-363. | MR 344713 | Zbl 0279.58005

[B] F. Browder, On the spectral theory of elliptic differential operators, I, Math. Annalen, Vol. 142, 1961, pp. 22-130. | MR 209909 | Zbl 0104.07502

[FV] S. Friedlander, and M. Vishik, Instability criteria for steady flows of a perfect fluid, Chaos, Vol. 2, 1992, No. 3, pp. 455-460. | MR 1184488 | Zbl 1055.76518

[G] N. Gunther, On the motion of fluid in a moving container, Isvestia Akad. Nauk SSSR. Ser. Fiz.-Mat., Vol. 20, 1927, pp. 1323-1348, 1503-1532; Ibid. Vol. 21, 1927, pp. 521-556, 735-756; Vol. 22, 1928, pp. 9-30.

[GS] Y. Guo, and W. Strauss, Nonlinear instability of double-humped equilibria, Ann. IHP (An. NL) (to appear). | Numdam | MR 1340268 | Zbl 0836.35130

[K] T. Kato, On classical solutions of the two-dimensional non-stationary Euler equation, Arch. Rat. Mech. Anal., Vol. 27, 1968, pp. 188-200. | MR 211057 | Zbl 0166.45302

[L] L. Lichtenstein, Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flussikeiten und die Helmgoltzschen Wirbelsalte, Math. Zeit., Vol. 23, 1925, pp. 89-154; Ibid. Vol. 26, 1927, pp. 196-323, 387-415, 723; Vol. 32, 1930, pp. 608. | JFM 51.0658.01 | MR 1544857

[Li] V. Liu, An example of instability for the Navier-Stokes equations on the 2-dimensional torus, Comm. in PDE's, Vol. 17, 1992, 11-12, pp. 1995-2012. | MR 1194747 | Zbl 0781.35054

[N] R. Nussbaum, The radius of the essential spectrum, Duke Math. J., Vol. 37, 1970, pp. 473-478. | MR 264434 | Zbl 0216.41602

[MS] L. Meshalkin, and Y. Sinai, Investigation of stability for a system of equations describing plane motion of a viscous incompressible fluid, Applied Math. and Mech., Vol. 25, 1961, pp. 1140-1143. | MR 137419 | Zbl 0108.39501

[T] R. Temam, Local existence of C∞ solutions of the Euler equations of incompressible perfect fluids, Lectures Notes in Math., 1976, Vol. 565, pp. 184-194. | MR 467033 | Zbl 0355.76017

[To] W. Tollmien, Ein allgemeines Kriterium der Instabilitat laminar geschwindigkeits verteilungen, Nachr. Ges. Wiss. Gottingen, Math. Phys. Kl. Fachgruppe I, Vol. 1, 1935, pp. 79-114. | JFM 61.0925.01

[Y] V. Yudovich, The Linearization Method in Hydrodynamical Stability Theory, Translations of Math. Monographs, Vol. 74, 1989, AMS 170 pp. | MR 1003607 | Zbl 0727.76039

[Yu] V. Yudovich, Example of secondary stationary flow or periodic flow appearing while a laminar flow of a viscous incompressible fluid loses its stability, Applied Math. and Mech., Vol. 29, 1965, No. 3, pp. 453-467. | Zbl 0148.22307

[V] M. Vishik, Spectrum of small oscillations of an ideal fluid and Lyapunov exponents preprint. | MR 1423046

[W] W. Wolibner, Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long, Math. Z., Vol. 37, 1933, pp. 698-726. | JFM 59.1447.02 | MR 1545430 | Zbl 0008.06901