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On the existence of vanishing at infinity symmetric solutions to the plane stationary exterior Navier–Stokes problem

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Abstract

We study a nonhomogeneous boundary-value problem for the steady-state Navier–Stokes equations in a two-dimensional exterior domain with two orthogonal symmetry axes. The existence of a solution which tends to zero uniformly at infinity is proved under suitable parity conditions on the data of the problem. The result is obtained for arbitrary values of the flux of the boundary datum.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225, Vilnius, Lithuania

    Konstantin Pileckas

  2. Dipartimento di Matematica, Seconda Università di Napoli, via Vivaldi 43, 81100, Caserta, Italy

    Remigio Russo

Authors
  1. Konstantin Pileckas
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  2. Remigio Russo
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Correspondence to Konstantin Pileckas.

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Pileckas, K., Russo, R. On the existence of vanishing at infinity symmetric solutions to the plane stationary exterior Navier–Stokes problem. Math. Ann. 352, 643–658 (2012). https://doi.org/10.1007/s00208-011-0653-4

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  • DOI: https://doi.org/10.1007/s00208-011-0653-4

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