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Algebra i Analiz, 2021, Volume 33, Issue 2, Pages 197–214 (Mi aa1752)  
This article is cited in 5 scientific papers (total in 5 papers)

Research Papers

Steady state non-Newtonian flow in thin tube structure: equation on the graph

G. Panasenkoab, K. Pileckasb, B. Vernescuc

a University of Lyon, UJM, Institute Camille Jordan UMR CNRS 5208, 23 rue P. Michelon, 42023, Saint-Etienne, France
b Faculty of Mathematics and Informatics, Institute of Applied Mathematics, Vilnius University, Naugarduko Str., 24, Vilnius, 03225 Lithuania
c Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA01609, USA
Full-text PDF (276 kB) Citations (5)
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Abstract: The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions in the vertices. Nonlinear equations on the graph generated by the non-Newtonian rheology are treated here. The existence and uniqueness of a solution of this problem is proved. This solution describes the leading term of an asymptotic analysis of the stationary non-Newtonian fluid motion in a thin tube structure with no-slip boundary condition on the lateral boundary.
Keywords: non-Newtonian flow, strain rate dependent viscosity, asymptotic dimension reduction, quasi-Poiseuille flows, equation on the graph.
Funding agency Grant number
ESF - European Social Fund 09.3.3-LMT-K-712-17-0003
This project has received funding from European Social Fund (project №09.3.3-LMT-K-712-17-0003) under grant agreement with the Research Council of Lithuania (LMTLT).
Received: 09.11.2020
English version:
St. Petersburg Mathematical Journal, 2022, Volume 33, Issue 2, Pages 327–340
DOI: https://doi.org/10.1090/spmj/1702
Document Type: Article
Language: English
Citation: G. Panasenko, K. Pileckas, B. Vernescu, “Steady state non-Newtonian flow in thin tube structure: equation on the graph”, Algebra i Analiz, 33:2 (2021), 197–214; St. Petersburg Math. J., 33:2 (2022), 327–340
Citation in format AMSBIB
\Bibitem{PanPilVer21}
\by G.~Panasenko, K.~Pileckas, B.~Vernescu
\paper Steady state non-Newtonian flow in thin tube structure: equation on the graph
\jour Algebra i Analiz
\yr 2021
\vol 33
\issue 2
\pages 197--214
\mathnet{http://mi.mathnet.ru/aa1752}
\transl
\jour St. Petersburg Math. J.
\yr 2022
\vol 33
\issue 2
\pages 327--340
\crossref{https://doi.org/10.1090/spmj/1702}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    References:29
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