Abstract
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 \(F=\int \limits _{\partial \Omega }\mathbf{a }\cdot \mathbf{n }dS\).
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The research was funded by a Grant No. S-MIP-17-68 from the Research Council of Lithuania.
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Kaulakytė, K., Klovienė, N. & Pileckas, K. Nonhomogeneous boundary value problem for the stationary Navier–Stokes equations in a domain with a cusp. Z. Angew. Math. Phys. 70, 36 (2019). https://doi.org/10.1007/s00033-019-1075-5
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DOI: https://doi.org/10.1007/s00033-019-1075-5