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arXiv · 1605.03864

On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains

Julien Guillod
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Abstract

The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis is valid if the steady solution is the sum of the critically decaying flux carrier with flux $|Φ| < 2π$ and a small subcritically decaying term. Under the central symmetry assumption, the general hypothesis is also proven for any critically decaying steady solutions under a suitable smallness condition.

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Julien Guillod. 2016-05-12. On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains. https://doi.org/10.1007/s00220-016-2794-5

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