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Three-dimensional instability of planar flows

Abstract : We study the stability of two-dimensional solutions of the three-dimensional Navier-Stokes equations, in the limit of small viscosity. We are interested in steady flows with locally closed streamlines. We consider the so-called elliptic and centrifugal instabilities, which correspond to the continuous spectrum of the underlying linearized Euler operator. Through the justification of highly oscillating Wentzel-Kramers-Brillouin expansions, we prove the nonlinear instability of such flows. The main difficulty is the control of nonoscillating and nonlocal perturbations issued from quadratic interactions.
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https://hal.archives-ouvertes.fr/hal-00458139
Contributor : Marie-Annick Guillemer <>
Submitted on : Friday, February 19, 2010 - 2:35:09 PM
Last modification on : Monday, October 12, 2020 - 10:27:28 AM

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  • HAL Id : hal-00458139, version 1

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François Gallaire, David Gérard-Varet, Frédéric Rousset. Three-dimensional instability of planar flows. Archive for Rational Mechanics and Analysis, Springer Verlag, 2007, 186 (3), pp.423-475. ⟨hal-00458139⟩

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