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Sbornik: Mathematics, 2014, Volume 205, Issue 6, Pages 763–776
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004397 (Mi sm8265) 		 
This article is cited in 20 scientific papers (total in 20 papers)

On steady motion of viscoelastic fluid of Oldroyd type

E. S. Baranovskii

Voronezh State University of Engineering Technologies
English version PDF (470 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2014v205n06ABEH004397
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.
Received: 20.06.2013 and 30.03.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 6, Pages 3–16
DOI: https://doi.org/10.4213/sm8265
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: Primary 35Q35; Secondary 35D30, 76A10
Language: English
Original paper language: Russian
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
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:258
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    References:131
    First page:209
     
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