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.
\Bibitem{Bar14}
\by E.~S.~Baranovskii
\paper On steady motion of viscoelastic fluid of Oldroyd type
\jour Sb. Math.
\yr 2014
\vol 205
\issue 6
\pages 763--776
\mathnet{http://mi.mathnet.ru/eng/sm8265}
\crossref{https://doi.org/10.1070/SM2014v205n06ABEH004397}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241826}
\zmath{https://zbmath.org/?q=an:06349850}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014SbMat.205..763B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000344080300001}
\elib{https://elibrary.ru/item.asp?id=21826626}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907364886}
Linking options:
https://www.mathnet.ru/eng/sm8265
https://doi.org/10.1070/SM2014v205n06ABEH004397
https://www.mathnet.ru/eng/sm/v205/i6/p3
This publication is cited in the following 24 articles:
Evgenii S. Baranovskii, Mikhail A. Artemov, Sergey V. Ershkov, Alexander V. Yudin, “The Kelvin–Voigt–Brinkman–Forchheimer Equations with Non-Homogeneous Boundary Conditions”, Mathematics, 13:6 (2025), 967
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia, “Multiplicative Control Problem for the Stationary Mass Transfer Model with Variable Coefficients”, Appl Math Optim, 90:2 (2024)
Evgenii S. Baranovskii, Anastasia A. Domnich, Mikhail A. Artemov, “Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties”, Mathematics, 12:21 (2024), 3337
Evgenii S. Baranovskii, Mikhail A. Artemov, “Topological Degree for Operators of Class (S)+ with Set-Valued Perturbations and Its New Applications”, Fractal Fract, 8:12 (2024), 738
Cesar A. Valencia, David A. Torres, Clara G. Hernández, Juan P. Escandón, Juan R. Gómez, René O. Vargas, “Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions”, Mathematics, 11:20 (2023), 4231
Na Li, Guangpu Zhao, Xue Gao, Ying Zhang, Yongjun Jian, “The Impacts of Viscoelastic Behavior on Electrokinetic Energy Conversion for Jeffreys Fluid in Microtubes”, Nanomaterials, 12:19 (2022), 3355
Evgenii S. Baranovskii, Mikhail A. Artemov, “Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit”, Polymers, 14:18 (2022), 3789
E. S. Baranovskii, “Steady flows of an oldroyd fluid with threshold slip”, Commun. Pure Appl. Anal, 18:2 (2019), 735–750
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
E. S. Baranovskii, M. A. Artemov, “Global existence results for Oldroyd fluids with wall slip”, Acta Appl. Math., 147:1 (2017), 197–210
E. S. Baranovskii, “On weak solutions to evolution equations of viscoelastic fluid flows”, J. Appl. Industr. Math., 11:2 (2017), 174–184
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
E. S. Baranovskii, A. A. Artemov, “Existence of optimal control for a nonlinear-viscous fluid model”, Int. J. Differ. Equ., 2016, 9428128, 6 pp.
E. S. Baranovskii, M. A. Artemov, “Ob odnoi modeli dvizheniya vyazkouprugoi zhidkosti s pristennym skolzheniem”, Sovremennye naukoemkie tekhnologii, 2016, no. 8-1, 27–31
M. A. Artemov, G. G. Berdzenishvili, “Global well-posedness for 2-D viscoelastic fluid model”, Appl. Math. Sci., 10:54 (2016), 2661–2670
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
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
M. A. Artemov, G. G. Berdzenishvili, A. P. Yakubenko, “Optimalnoe upravlenie sistemoi, opisyvayuschei techenie vyazkouprugoi sredy”, Mezhdunarodnyi zhurnal eksperimentalnogo obrazovaniya, 2015, 460–460
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.
“Mixed Boundary-Value Problems For Motion Equations of a Viscoelastic Medium”, Electron. J. Differ. Equ., 2015, 252
Citation in format AMSBIB
Contact us: