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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 306, Pages 210–228 (Mi znsl857)  
This article is cited in 5 scientific papers (total in 5 papers)

Steady-state solutions to the equations of motion of second-grade fluids with general Navier-type slip boundary conditions in Hölder spaces

A. Tania, C. Le Rouxbc

a Department of Mathematics, Faculty of Science and Technology, Keio University
b University of Pretoria
c University of Pretoria, Faculty of Natural and Agricultural Sciences
Full-text PDF (216 kB) Citations (5)
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Abstract: We consider a boundary-value problem for the stationary flow of an incompressible second-grade fluid in a bounded domain. The boundary condition allows for no-slip, Navier-type slip and free slip on different parts of the boundary.
We first establish the well-posedness of a linear auxiliary problem by means of a fixed-point argument in which it is decomposed into a Stokes-type problem and two transport equations. Then we use the method of successive approximations to prove the unique solvability in Hölder spaces of the nonlinear problem with a sufficiently small body force.
Received: 21.11.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 130, Issue 4, Pages 4899–4909
DOI: https://doi.org/10.1007/s10958-005-0385-7
Bibliographic databases:
UDC: 517
Language: English
Citation: A. Tani, C. Le Roux, “Steady-state solutions to the equations of motion of second-grade fluids with general Navier-type slip boundary conditions in Hölder spaces”, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Zap. Nauchn. Sem. POMI, 306, POMI, St. Petersburg, 2003, 210–228; J. Math. Sci. (N. Y.), 130:4 (2005), 4899–4909
Citation in format AMSBIB
\Bibitem{TanLe 03}
\by A.~Tani, C.~Le~Roux
\paper Steady-state solutions to the equations of motion of second-grade fluids with general Navier-type slip boundary conditions in H\"older spaces
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~34
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 306
\pages 210--228
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl857}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2065505}
\zmath{https://zbmath.org/?q=an:1148.35345}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 130
\issue 4
\pages 4899--4909
\crossref{https://doi.org/10.1007/s10958-005-0385-7}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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