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On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

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Abstract

We study the stability of some exact stationary solutions to the two-dimensional Navier–Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small L 2 perturbations.

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  1. Yasunori Maekawa

    Present address: Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

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  1. Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba, Sendai, 980-8578, Japan

    Yasunori Maekawa

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  1. Yasunori Maekawa
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Correspondence to Yasunori Maekawa.

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Communicated by V. Šverák

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Maekawa, Y. On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk. Arch Rational Mech Anal 225, 287–374 (2017). https://doi.org/10.1007/s00205-017-1105-4

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