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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 397, Pages 73–88 (Mi znsl4668)  

This article is cited in 4 scientific papers (total in 4 papers)

Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation

A. Mikhaylov, S. Repin

St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (229 kB) Citations (4)
References:
Abstract: Vorticity-velocity-pressure formulation for the stationary Stokes problem in 2D is considered. We analyze the corresponding generalized formulation, establish sufficient conditions that guarantee existence of the generalized solution and deduce estimates of the difference between the exact solution (i.e., exact velocity, vorticity, and pressure) and an arbitrary approximating function (velocity, vorticity, pressure) that belongs to the corresponding functional class and satisfies the boundary conditions. For this purpose we use the method suggested in [10, 12], which is based on transformations of the integral identity that defines the corresponding generalized solution.
Key words and phrases: Stokes problem, viscous incompressible fluids, estimates of deviations from exact solutions.
Received: 03.11.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 5, Pages 698–706
DOI: https://doi.org/10.1007/s10958-012-0953-6
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: A. Mikhaylov, S. Repin, “Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation”, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Zap. Nauchn. Sem. POMI, 397, POMI, St. Petersburg, 2011, 73–88; J. Math. Sci. (N. Y.), 185:5 (2012), 698–706
Citation in format AMSBIB
\Bibitem{MikRep11}
\by A.~Mikhaylov, S.~Repin
\paper Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 397
\pages 73--88
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4668}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870109}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 185
\issue 5
\pages 698--706
\crossref{https://doi.org/10.1007/s10958-012-0953-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866892296}
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  • https://www.mathnet.ru/eng/znsl/v397/p73
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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