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Mat. Sb., 2014, Volume 205, Number 6, Pages 3–16 (Mi msb8265)  

This article is cited in 17 scientific papers (total in 17 papers)

On steady motion of viscoelastic fluid of Oldroyd type

E. S. Baranovskii

Voronezh State University of Engineering Technologies

Abstract: We consider a mathematical model describing the steady motion of a viscoelastic medium of Oldroyd type under the Navier slip condition at the boundary. In the rheological relation, we use the objective regularized Jaumann derivative. We prove the solubility of the corresponding boundary-value problem in the weak setting. We obtain an estimate for the norm of a solution in terms of the data of the problem. We show that the solution set is sequentially weakly closed. Furthermore, we give an analytic solution of the boundary-value problem describing the flow of a viscoelastic fluid in a flat channel under a slip condition at the walls.
Bibliography: 13 titles.

Keywords: non-Newtonian fluids, viscoelastic media, Oldroyd model, Navier slip condition, flow in a channel.


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English version:
Sbornik: Mathematics, 2014, 205:6, 763–776

Bibliographic databases:

UDC: 517.958
MSC: Primary 35Q35; Secondary 35D30, 76A10
Received: 20.06.2013 and 30.03.2014

Citation: E. S. Baranovskii, “On steady motion of viscoelastic fluid of Oldroyd type”, Mat. Sb., 205:6 (2014), 3–16; Sb. Math., 205:6 (2014), 763–776

Citation in format AMSBIB
\by E.~S.~Baranovskii
\paper On steady motion of viscoelastic fluid of Oldroyd type
\jour Mat. Sb.
\yr 2014
\vol 205
\issue 6
\pages 3--16
\jour Sb. Math.
\yr 2014
\vol 205
\issue 6
\pages 763--776

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    This publication is cited in the following articles:
    1. E. A. Lyzhnik, “Effektivnye otsenki reshenii uravnenii dvizheniya vyazkouprugoi zhidkosti”, Mezhdunarodnyi zhurnal prikladnykh i fundamentalnykh issledovanii, 2014, no. 8-4, 150–151  elib
    2. A. V. Kozlova, “Ob odnom prilozhenii integro-differentsialnykh uravnenii Volterra”, Sovremennye metody prikladnoi matematiki, teorii upravleniya i kompyuternykh tekhnologii, Sbornik trudov VII mezhdunarodnoi konferentsii PMTUKT-2014, Nauchnaya kniga, Voronezh, 2014, 198–199  elib
    3. K. E. Sharapov, “K zadache o dvizhenii zhidkosti Dzheffrisa v kanale”, Sovremennye naukoemkie tekhnologii, 2014, no. 9, 93  elib
    4. E. A. Lyzhnik, “Tormozhenie techeniya polimernoi zhidkosti v ploskom kanale”, Mezhdunarodnyi zhurnal prikladnykh i fundamentalnykh issledovanii, 2014, no. 9-3, 168  elib
    5. V. A. Kozlov, S. A. Nazarov, “One-dimensional model of viscoelastic blood flow through a thin elastic vessel”, J. Math. Sci., 207:2 (2015), 249–269  crossref  mathscinet  zmath  scopus
    6. M. A. Artemov, E. S. Baranovskii, “Mixed boundary-value problems for motion equations of a viscoelastic medium”, Electron. J. Differential Equations, 2015:252 (2015), 1–9  mathscinet  elib  scopus
    7. M. A. Artemov, G. G. Berdzenishvili, A. P. Yakubenko, “Optimalnoe upravlenie sistemoi, opisyvayuschei techenie vyazkouprugoi sredy”, Mezhdunarodnyi zhurnal eksperimentalnogo obrazovaniya, 2015, 460–460  elib
    8. E. S. Baranovskii, “Existence results for regularized equations of second-grade fluids with wall slip”, Electron. J. Qual. Theory Differ. Equ., 2015, 91, 12 pp.  crossref  mathscinet  zmath  isi  scopus
    9. “Mixed Boundary-Value Problems For Motion Equations of a Viscoelastic Medium”, Electron. J. Differ. Equ., 2015, 252  isi
    10. E. S. Baranovskii, “Mixed initial-boundary value problem for equations of motion of Kelvin–Voigt fluids”, Comput. Math. Math. Phys., 56:7 (2016), 1363–1371  mathnet  crossref  crossref  isi  elib
    11. E. S. Baranovskii, A. A. Artemov, “Existence of optimal control for a nonlinear-viscous fluid model”, Int. J. Differ. Equ., 2016, 9428128, 6 pp.  crossref  mathscinet  zmath  isi  scopus
    12. E. S. Baranovskii, M. A. Artemov, “Ob odnoi modeli dvizheniya vyazkouprugoi zhidkosti s pristennym skolzheniem”, Sovremennye naukoemkie tekhnologii, 2016, no. 8-1, 27–31  elib
    13. M. A. Artemov, G. G. Berdzenishvili, “Global well-posedness for 2-D viscoelastic fluid model”, Appl. Math. Sci., 10:54 (2016), 2661–2670  crossref  elib  scopus
    14. E. S. Baranovskii, M. A. Artemov, “Global existence results for Oldroyd fluids with wall slip”, Acta Appl. Math., 147:1 (2017), 197–210  crossref  mathscinet  zmath  isi  elib  scopus
    15. E. S. Baranovskii, “On weak solutions to evolution equations of viscoelastic fluid flows”, J. Appl. Industr. Math., 11:2 (2017), 174–184  mathnet  crossref  crossref  elib
    16. E. S. Baranovskii, “On flows of viscoelastic fluids under threshold-slip boundary conditions”, International Conference Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 973, IOP Publishing Ltd, 2018, UNSP 012051  crossref  isi  scopus
    17. Baranovskii E.S., “Steady Flows of An Oldroyd Fluid With Threshold Slip”, Commun. Pure Appl. Anal, 18:2 (2019), 735–750  crossref  mathscinet  zmath  isi  scopus
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