### A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of $SU\left(2\right)$ connections.

Himpel, Benjamin (2005)

Geometry & Topology

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Himpel, Benjamin (2005)

Geometry & Topology

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Avila, Artur, Viana, Marcelo (2005)

Portugaliae Mathematica. Nova Série

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Jiří Adámek, Václav Koubek (1971)

Commentationes Mathematicae Universitatis Carolinae

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Saroop Kaul (1987)

Fundamenta Mathematicae

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Miroslav Krutina (1989)

Commentationes Mathematicae Universitatis Carolinae

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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...