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A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain

Author

Listed:
  • Kristina Kaulakytė

    (Institute of Applied Mathematics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

  • Konstantinas Pileckas

    (Institute of Applied Mathematics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

Abstract

The boundary value problem for the steady Navier–Stokes system is considered in a 2 D multiply-connected bounded domain with the boundary having a power cusp singularity at the point O . The case of a boundary value with nonzero flow rates over connected components of the boundary is studied. It is also supposed that there is a source/sink in O . In this case the solution necessarily has an infinite Dirichlet integral. The existence of a solution to this problem is proved assuming that the flow rates are “sufficiently small”. This condition does not require the norm of the boundary data to be small. The solution is constructed as the sum of a function with the finite Dirichlet integral and a singular part coinciding with the asymptotic decomposition near the cusp point.

Suggested Citation

  • Kristina Kaulakytė & Konstantinas Pileckas, 2021. "A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain," Mathematics, MDPI, vol. 9(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2022-:d:620458
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