### Differentiability, rigidity and Godbillon-Vey classes for Anosov flows

S. Hurder, Anatoly Katok (1990)

Publications Mathématiques de l'IHÉS

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S. Hurder, Anatoly Katok (1990)

Publications Mathématiques de l'IHÉS

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Mark Pollicott (1991-1992)

Séminaire de théorie spectrale et géométrie

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Mark Pollicott (1991)

Séminaire de théorie spectrale et géométrie

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Alexander Shnirelman (1999-2000)

Séminaire Équations aux dérivées partielles

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Boris Khesin (2002-2003)

Séminaire Équations aux dérivées partielles

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We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [].

Alejandro Kocsard (2009)

Annales de l'I.H.P. Analyse non linéaire

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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 ${L}^{2}$ 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...