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Non-Isothermal Creeping Flows in a Pipeline Network : Existence Results. / Baranovskii, Evgenii S.; Provotorov, Vyacheslav V.; Artemov, Mikhail A.; Zhabko, Alexey P.

In: Symmetry-Basel, Vol. 13, No. 7, 1300, 19.07.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranovskii, ES, Provotorov, VV, Artemov, MA & Zhabko, AP 2021, 'Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results', Symmetry-Basel, vol. 13, no. 7, 1300. https://doi.org/10.3390/sym13071300

APA

Baranovskii, E. S., Provotorov, V. V., Artemov, M. A., & Zhabko, A. P. (2021). Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results. Symmetry-Basel, 13(7), [1300]. https://doi.org/10.3390/sym13071300

Vancouver

Baranovskii ES, Provotorov VV, Artemov MA, Zhabko AP. Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results. Symmetry-Basel. 2021 Jul 19;13(7). 1300. https://doi.org/10.3390/sym13071300

Author

Baranovskii, Evgenii S. ; Provotorov, Vyacheslav V. ; Artemov, Mikhail A. ; Zhabko, Alexey P. / Non-Isothermal Creeping Flows in a Pipeline Network : Existence Results. In: Symmetry-Basel. 2021 ; Vol. 13, No. 7.

BibTeX

@article{ed3e2f6af14241f59b7f3d17efb11c33,
title = "Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results",
abstract = "This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.",
keywords = "pipeline network, non-isothermal flows, temperature-dependent viscosity, pressure boundary conditions, weak solutions, large-date existence, OPTIMAL BOUNDARY CONTROL, NAVIER-STOKES EQUATIONS, GAS-FLOW, ASYMPTOTIC ANALYSIS, RIEMANN PROBLEM, MODEL, SYSTEM, Large-date existence, Pipeline network, Non-isothermal flows, Weak solutions, Pressure boundary conditions, Temperature-dependent viscosity",
author = "Baranovskii, {Evgenii S.} and Provotorov, {Vyacheslav V.} and Artemov, {Mikhail A.} and Zhabko, {Alexey P.}",
note = "Baranovskii, E.S.; Provotorov, V.V.; Artemov, M.A.; Zhabko, A.P. Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results. Symmetry 2021, 13, 1300. https://doi.org/10.3390/sym13071300",
year = "2021",
month = jul,
day = "19",
doi = "10.3390/sym13071300",
language = "English",
volume = "13",
journal = "Symmetry",
issn = "2073-8994",
publisher = "MDPI AG",
number = "7",

}

RIS

TY - JOUR

T1 - Non-Isothermal Creeping Flows in a Pipeline Network

T2 - Existence Results

AU - Baranovskii, Evgenii S.

AU - Provotorov, Vyacheslav V.

AU - Artemov, Mikhail A.

AU - Zhabko, Alexey P.

N1 - Baranovskii, E.S.; Provotorov, V.V.; Artemov, M.A.; Zhabko, A.P. Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results. Symmetry 2021, 13, 1300. https://doi.org/10.3390/sym13071300

PY - 2021/7/19

Y1 - 2021/7/19

N2 - This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

AB - This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

KW - pipeline network

KW - non-isothermal flows

KW - temperature-dependent viscosity

KW - pressure boundary conditions

KW - weak solutions

KW - large-date existence

KW - OPTIMAL BOUNDARY CONTROL

KW - NAVIER-STOKES EQUATIONS

KW - GAS-FLOW

KW - ASYMPTOTIC ANALYSIS

KW - RIEMANN PROBLEM

KW - MODEL

KW - SYSTEM

KW - Large-date existence

KW - Pipeline network

KW - Non-isothermal flows

KW - Weak solutions

KW - Pressure boundary conditions

KW - Temperature-dependent viscosity

UR - http://www.scopus.com/inward/record.url?scp=85111381355&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/35e475ab-d8d2-35d4-9e55-24c01a0ba29b/

U2 - 10.3390/sym13071300

DO - 10.3390/sym13071300

M3 - Article

VL - 13

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 7

M1 - 1300

ER -

ID: 86577916