On the -instability of fluid flows
Alexander Shnirelman (1999-2000)
Séminaire Équations aux dérivées partielles
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Displaying similar documents to “Vector fields generating more than one flow.”
On the -instability of fluid flows
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On the -instability and -controllability of steady flows of an ideal incompressible fluid
Alexander Shnirelman (1999)
Journées équations aux dérivées partielles
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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 vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...