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

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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. Panasenko^ab, K. Pileckas^b, B. Vernescu^c

^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

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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}

Linking options:

https://www.mathnet.ru/eng/aa1752

https://www.mathnet.ru/eng/aa/v33/i2/p197

This publication is cited in the following 5 articles:

Grigory Panasenko, Konstantin Pileckas, “Partial Asymptotic Dimension Reduction for Steady State Non-Newtonian Flow with Strain Rate Dependent Viscosity in Thin Tube Structure”, J. Math. Fluid Mech., 25:1 (2023)
Nikolajus Kozulinas, Grigory Panasenko, Konstantinas Pileckas, Vytenis Šumskas, “NUMERICAL STUDY OF THE EQUATION ON THE GRAPH FOR THE STEADY STATE NON-NEWTONIAN FLOW IN THIN TUBE STRUCTURE”, Mathematical Modelling and Analysis, 28:4 (2023), 581
Bunoiu R., Gaudiello A., “On the Bingham Flow in a Thin Y-Like Shaped Structure”, J. Math. Fluid Mech., 24:1 (2022), 20
E. S. Baranovskii, “Feedback Optimal Control Problem for a Network Model of Viscous Fluid Flows”, Math. Notes, 112:1 (2022), 26–39
Baranovskii E.S., Provotorov V.V., Artemov M.A., Zhabko A.P., “Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results”, Symmetry-Basel, 13:7 (2021), 1300

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

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