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On the Existence and Uniqueness of an R ν -Generalized Solution to the Stokes Problem with Corner Singularity

Author

Listed:
  • Viktor A. Rukavishnikov

    (Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia
    These authors contributed equally to this work.)

  • Alexey V. Rukavishnikov

    (Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia
    These authors contributed equally to this work.)

Abstract

We consider the Stokes problem with the homogeneous Dirichlet boundary condition in a polygonal domain with one re-entrant corner on its boundary. We define an R ν -generalized solution of the problem in a nonsymmetric variational formulation. Such defined solution allows us to construct numerical methods for finding an approximate solution without loss of accuracy. In the paper, the existence and uniqueness of an R ν -generalized solution in weighted sets is proved.

Suggested Citation

  • Viktor A. Rukavishnikov & Alexey V. Rukavishnikov, 2022. "On the Existence and Uniqueness of an R ν -Generalized Solution to the Stokes Problem with Corner Singularity," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1752-:d:820602
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