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A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier–Stokes equations in 2D

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We show that a velocity field u satisfying the stationary Navier–Stokes equations on the entire plane must be constant under the growth condition lim sup |x|−α|u(x)| < ∞ as |x| → ∞ for some α ∈ [0, 1/7).† Bibliography: 10 titles.

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References

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Authors and Affiliations

  1. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D–66041, Saarbrücken, Germany

    M. Fuchs

  2. University of Jyväskylä, P.O.Box 35(MaD), FI-40014, Jyväskylä, Finland

    X. Zhong

Authors
  1. M. Fuchs
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  2. X. Zhong
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Correspondence to M. Fuchs.

Additional information

† Actually, the case α < 1/3 is sufficient (cf. Note Added in Proof below).

Translated from Problems in Mathematical Analysis 60, September 2011, pp. 111–118.

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Fuchs, M., Zhong, X. A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier–Stokes equations in 2D . J Math Sci 178, 695–703 (2011). https://doi.org/10.1007/s10958-011-0578-1

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  • DOI: https://doi.org/10.1007/s10958-011-0578-1

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