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Zap. Nauchn. Sem. POMI, 2000, Volume 271, Pages 224–275 (Mi znsl1358)  

This article is cited in 5 scientific papers (total in 5 papers)

Initial boundary-value problem for generalized Stokes equations in the half-space

V. A. Solonnikov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The paper contains construction of the solution of the Cauchy–Dirichlet problem in the half-space $\mathbb R^3_+$ for a family of systems of differential equations containing the Stokes system. For this solution coercive estimates in the Hölder spaces of functions are obtained.

Full text: PDF file (418 kB)

English version:
Journal of Mathematical Sciences (New York), 2003, 115:6, 2832–2861

Bibliographic databases:

UDC: 517
Received: 24.08.2000

Citation: V. A. Solonnikov, “Initial boundary-value problem for generalized Stokes equations in the half-space”, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Zap. Nauchn. Sem. POMI, 271, POMI, St. Petersburg, 2000, 224–275; J. Math. Sci. (N. Y.), 115:6 (2003), 2832–2861

Citation in format AMSBIB
\Bibitem{Sol00}
\by V.~A.~Solonnikov
\paper Initial boundary-value problem for generalized Stokes equations in the half-space
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 271
\pages 224--275
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1358}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1810619}
\zmath{https://zbmath.org/?q=an:1027.76010}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 6
\pages 2832--2861
\crossref{https://doi.org/10.1023/A:1023382122038}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Solonnikov V.A., “Lectures on evolution free boundary problems: Classical solutions”, Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics, 1812, 2003, 123–175  crossref  mathscinet  zmath  isi
    2. J. Math. Sci. (N. Y.), 143:2 (2007), 2969–2986  mathnet  crossref  mathscinet  zmath
    3. St. Petersburg Math. J., 26:6 (2015), 985–1003  mathnet  crossref  mathscinet  isi  elib  elib
    4. Chang T. Jin B.J., “Initial and Boundary Value Problem of the Unsteady Navier–Stokes System in the Half-Space With Holder Continuous Boundary Data”, J. Math. Anal. Appl., 433:2 (2016), 1846–1869  crossref  mathscinet  zmath  isi  scopus
    5. Chang T. Kang K., “Solvability For Stokes System in Holder Spaces in Bounded Domains and Its Applications”, J. Math. Fluid Mech., 20:4 (2018), 1857–1888  crossref  mathscinet  zmath  isi  scopus
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