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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 410, Pages 5–24 (Mi znsl5622)  
This article is cited in 6 scientific papers (total in 6 papers)

Estimates of solutions to the perturbed Stokes system

V. Vialova, T. Shilkinb

a С.-Петербургский государственный университет, Университетский пр., 28, Старый Петергоф, 198504, С.-Петербург, Россия
b С.-Петербургское отделение Математического института им. В. А. Стеклова РАН, Фонтанка, 27, 191023, С.-Петербург, Россия
Full-text PDF (287 kB) Citations (6)
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Abstract: In this paper, we derive local estimates of solutions to the Perturbed Stokes system, which arises as a reduction of the Stokes system near a curved part of the boundary of the domain if a diffeomorphism flatting the boundary is applied. The estimates obtained in the paper play the crucial role in the investigation of partial regularity of weak solutions to the Navier–Stokes system near a curved part of the boundary.
Key words and phrases: Stokes system, boundary regularity.
Received: 17.12.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 195, Issue 1, Pages 1–12
DOI: https://doi.org/10.1007/s10958-013-1560-x
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: V. Vialov, T. Shilkin, “Estimates of solutions to the perturbed Stokes system”, Boundary-value problems of mathematical physics and related problems of function theory. Part 43, Zap. Nauchn. Sem. POMI, 410, POMI, St. Petersburg, 2013, 5–24; J. Math. Sci. (N. Y.), 195:1 (2013), 1–12
Citation in format AMSBIB
\Bibitem{VyaShi13}
\by V.~Vialov, T.~Shilkin
\paper Estimates of solutions to the perturbed Stokes system
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 410
\pages 5--24
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5622}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3048259}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 195
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1007/s10958-013-1560-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899013396}
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  • https://www.mathnet.ru/eng/znsl/v410/p5
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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