In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in
@incollection{JEDP_1999____A13_0, author = {Shnirelman, Alexander}, title = {On the ${L}^2$-instability and ${L}^2$-controllability of steady flows of an ideal incompressible fluid}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {13}, pages = {1--8}, publisher = {Universit\'e de Nantes}, year = {1999}, zbl = {01810586}, mrnumber = {1718998}, language = {en}, url = {http://www.numdam.org/item/JEDP_1999____A13_0/} }
TY - JOUR AU - Shnirelman, Alexander TI - On the ${L}^2$-instability and ${L}^2$-controllability of steady flows of an ideal incompressible fluid JO - Journées équations aux dérivées partielles PY - 1999 SP - 1 EP - 8 PB - Université de Nantes UR - http://www.numdam.org/item/JEDP_1999____A13_0/ LA - en ID - JEDP_1999____A13_0 ER -
%0 Journal Article %A Shnirelman, Alexander %T On the ${L}^2$-instability and ${L}^2$-controllability of steady flows of an ideal incompressible fluid %J Journées équations aux dérivées partielles %D 1999 %P 1-8 %I Université de Nantes %U http://www.numdam.org/item/JEDP_1999____A13_0/ %G en %F JEDP_1999____A13_0
Shnirelman, Alexander. On the ${L}^2$-instability and ${L}^2$-controllability of steady flows of an ideal incompressible fluid. Journées équations aux dérivées partielles (1999), article no. 13, 8 p. http://www.numdam.org/item/JEDP_1999____A13_0/
[A1] Sur la Géométrie diffé rentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier 16 (1966), 316-361. | Numdam | MR | Zbl
,[A2] On the a priori estimate in the theory of hydrodynamical stability, Amer. Math. Soc. Transl. 19 (1969), 267-269. | Zbl
,[A3] Mathematical methods of classical mechanics, Springer-Verlag, New York, 1989. | MR | Zbl
,[A-K] Topological methods in hydrodynamics, Applied Mathematical Sciences, v. 125, Springer-verlag, 1998. | MR | Zbl
, ,[B] The least action principle and the related concept of generalized flows for incompressible perfect fluids, J. Amer. Math. Soc. 2 (1989), no. 2, 225-255. | MR | Zbl
,[M-P] Mathematical theory of incompressible nonviscous fluids, Applied Mathematical Sciences, v. 96, Springer-Verlag, 1994. | MR | Zbl
, ,[S] The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Math. USSR Sbornik 56 (1987), no. 1, 79-105. | Zbl
,