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

Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
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Viktor A. Rukavishnikov: Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia
Alexey V. Rukavishnikov: Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia

Mathematics, 2022, vol. 10, issue 10, 1-14

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.

Keywords: R? -generalized solution; corner singularity; Stokes problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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