Nonhomogeneous boundary value problem for the stationary Navier–Stokes equations in a domain with a cusp

  • Kristina Kaulakytė
  • Neringa Klovienė
  • Konstantin PileckasEmail author


The nonhomogeneous boundary value problem for the stationary Navier–Stokes equations in a two-dimensional domain with a cusp point on the boundary is studied. The case when the flux of the boundary value \(\mathbf{a }\) is nonzero, i.e., when there is a source or sink in the cusp point, is considered. The existence of at least one weak solution having infinite Dirichlet integral is proved without any restrictions on the size of the flux \(F=\int \limits _{\partial \Omega }\mathbf{a }\cdot \mathbf{n }dS\).


Stationary Navier–Stokes equations Nonhomogeneous boundary condition Cusp point singularity Nonzero flux 

Mathematics Subject Classification

35Q30 76D03 76D05 



The research was funded by a Grant No. S-MIP-17-68 from the Research Council of Lithuania.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kristina Kaulakytė
    • 1
  • Neringa Klovienė
    • 1
  • Konstantin Pileckas
    • 1
    Email author
  1. 1.Institute of Applied MathematicsVilnius UniversityVilniusLithuania

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