Abstract
The linearized dynamics of an ideal fluid is shown to have an infinite set of invariants different from the usual Casimir invariants. The procedure of their construction is described. The inclusion of one or several such invariants makes it possible to obtain a sufficient condition for the stability of flows of the fluid in the framework of usual or magnetic hydrodynamics. The condition appears to be softer (closer to a necessary condition) than the previously known conditions.
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V. I. Ilgisonis, physics/0506073.
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Translated from Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 82, No. 9, 2005, pp. 647–651.
Original Russian Text Copyright © 2005 by Ilgisonis, Khalzov.