# On Convergence of Arbitrary *D*-Solution of Steady Navier–Stokes System in 2*D* Exterior Domains

## Abstract

We study solutions to stationary Navier–Stokes system in a two dimensional exterior domain. We prove that any such solution with a finite Dirichlet integral converges to a constant vector at infinity uniformly. No additional conditions (on symmetry or smallness, etc.) are assumed. In the proofs we develop the ideas of the classical papers of Gilbarg and Weinberger (Ann Sc Norm Pisa (4) 5:381–404, 1978) and Amick (Acta Math 161:71–130, 1988).

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## Notes

### Acknowledgements

The authors are grateful to the anonymous referee for many useful remarks and suggestions. M. Korobkov was partially supported by the Ministry of Education and Science of the Russian Federation (Grant 14.Z50.31.0037) and by the Russian Federation for Basic Research (Project Numbers 18-01-00649 and 17-01-00875). The research of K. Pileckas was funded by the Grant No. S-MIP-17-68 from the Research Council of Lithuania.

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### Conflict of interest

The authors declare that they have no conflict of interest.

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