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Note on the fast decay property of steady Navier–Stokes flows in the whole space

  • Tomoyuki Nakatsuka EMAIL logo
Published/Copyright: March 21, 2018

Abstract

We investigate the pointwise asymptotic behavior of solutions to the stationary Navier–Stokes equation in n (n3). We show the existence of a unique solution {u,p} such that |ju(x)|=O(|x|1-n-j) and |kp(x)|=O(|x|-n-k) (j,k=0,1,) as |x|, assuming the smallness of the external force and the rapid decay of its derivatives. The solution {u,p} decays more rapidly than the Stokes fundamental solution.

MSC 2010: 35Q30; 76D05

Funding statement: The research was supported by the Academy of Sciences of the Czech Republic, Institute of Mathematics (RVO: 67985840).

Acknowledgements

The author would like to thank Professor J. Neustupa for helpful conversations.

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Received: 2017-3-1
Revised: 2017-10-12
Accepted: 2018-3-1
Published Online: 2018-3-21
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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