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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 110–115
DOI: https://doi.org/10.4213/mzm11330 (Mi mzm11330) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Dirichlet Problem for the Stokes Equation

V. V. Pukhnachovab

a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.4213/mzm11330
Abstract: The paper presents some coercive a priori estimates of the solution of the Dirichlet problem for the linear Stokes equation relating vorticity and the stream function of an axially symmetric flow of an incompressible fluid. This equation degenerates on the axis of symmetry. The method used to obtain the estimates is based on a differential substitution transforming the Stokes equation into the Laplace equation and on the subsequent transition from cylindrical to Cartesian coordinates in three-dimensional space.
Keywords: flow-through problem, Stokes equation, coercive a priori estimates.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-8146.2016.1
Received: 28.07.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 132–136
DOI: https://doi.org/10.1134/S0001434617010138
Bibliographic databases:
Document Type: Article
UDC: 517.59+532.517
Language: Russian
Citation: V. V. Pukhnachov, “Dirichlet Problem for the Stokes Equation”, Mat. Zametki, 101:1 (2017), 110–115; Math. Notes, 101:1 (2017), 132–136
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v101/i1/p110
    • This publication is cited in the following 1 articles:
    1. K. Yu. Malyshev, E. A. Mikhaylov, I. O. Teplyakov, “Rapidly convergent series for solving the electrovortex flow problem in a hemispherical vessel”, Comput. Math. Math. Phys., 62:7 (2022), 1158–1170  mathnet  mathnet  crossref  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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