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Asymptotic Stability of Landau Solutions to Navier–Stokes System

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Abstract

It is known that the three-dimensional Navier–Stokes system for an incompressible fluid in the whole space has a one parameter family of explicit stationary solutions that are axisymmetric and homogeneous of degree −1. We show that these solutions are asymptotically stable under any L 2-perturbation.

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Authors and Affiliations

  1. Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Grzegorz Karch & Dominika Pilarczyk

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  1. Grzegorz Karch
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  2. Dominika Pilarczyk
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Correspondence to Grzegorz Karch.

Additional information

Communicated by V. Šverák

This work was partially supported by the MNiSzW grants No. N N201 365736 and N N201 418839, and the Foundation for Polish Science operated within the Innovative Economy Operational Programme 2007–2013 funded by European Regional Development Fund (Ph.D. Programme: Mathematical Methods in Natural Sciences).

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Karch, G., Pilarczyk, D. Asymptotic Stability of Landau Solutions to Navier–Stokes System. Arch Rational Mech Anal 202, 115–131 (2011). https://doi.org/10.1007/s00205-011-0409-z

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