Exact Solutions of Second-Grade Fluid Equations Full article
| Journal |
Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 |
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| Output data | Year: 2023, Volume: 322, Pages: 173-187 Pages count : 15 DOI: 10.1134/S0081543823040156 | ||||||
| Tags | SECOND-GRADE FLUID, FREE BOUNDARY PROBLEMS, LAYERED flOWS, BOUNDARY LAYER, HELICAL MOTIONS | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0001 |
Abstract:
The second-grade fluid equations describe the motion of relaxing fluids such as aqueous solutions of polymers. The existence and uniqueness of solutions to the initial–boundary value problems for these equations were studied by D. Cioranescu, V. Girault, C. Le Roux, A. Tani, G. P. Galdi, and others. However, their studies do not contain information about the qualitative properties of solutions of these equations. Such information can be obtained by analyzing their exact solutions, which is the main goal of this work. We study layered flows and a model problem with a free boundary, construct an analog of T. Kármán's solution, which describes the stationary motion of a second-grade fluid in a half-space induced by the rotation of the plane bounding it, and propose a generalization of V. A. Steklov's solution of the problem on unsteady helical flows of a Newtonian fluid to the case of a second-grade fluid.
Cite:
Petrova A.G.
, Pukhnachev V.V.
, Frolovskaya O.A.
Exact Solutions of Second-Grade Fluid Equations
Proceedings of the Steklov Institute of Mathematics. 2023. V.322. P.173-187. DOI: 10.1134/S0081543823040156 WOS Scopus РИНЦ OpenAlex
Exact Solutions of Second-Grade Fluid Equations
Proceedings of the Steklov Institute of Mathematics. 2023. V.322. P.173-187. DOI: 10.1134/S0081543823040156 WOS Scopus РИНЦ OpenAlex
Original:
Петрова А.Г.
, Пухначев В.В.
, Фроловская О.А.
Точные решения уравнений жидкости второго порядка
ТРУДЫ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМЕНИ В.А. СТЕКЛОВА. 2023. Т.322. С.180-194. DOI: 10.4213/tm4336 РИНЦ OpenAlex
Точные решения уравнений жидкости второго порядка
ТРУДЫ МАТЕМАТИЧЕСКОГО ИНСТИТУТА ИМЕНИ В.А. СТЕКЛОВА. 2023. Т.322. С.180-194. DOI: 10.4213/tm4336 РИНЦ OpenAlex
Dates:
| Submitted: | Dec 1, 2022 |
| Accepted: | Mar 20, 2023 |
| Published print: | Dec 20, 2023 |
Identifiers:
| Web of science: | WOS:001127223100012 |
| Scopus: | 2-s2.0-85180234830 |
| Elibrary: | 63436443 |
| OpenAlex: | W4390002498 |