Email this article 
THE PROBLEM OF THE FLOW OF ONE TYPE OF NON-NEWTONIAN FLUID THROUGH THE BOUNDARY OF A MULTI-CONNECTED DOMAIN
- Authors: Zvyagin V.G.1, Orlov V.P.1
-
Affiliations:
- Voronezh State University
- Issue: Vol 510, No 1 (2023)
- Pages: 33-38
- Section: MATHEMATICS
- URL: https://journal-vniispk.ru/2686-9543/article/view/134358
- DOI: https://doi.org/10.31857/S2686954323600064
- EDN: https://elibrary.ru/XHWKXX
- ID: 134358
Cite item
Open Access
Access granted
Subscription Access
Abstract
In this paper, the existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-newtonian fluid in a multi-connected domain with memory along the trajectories of a non-smooth velocity field and an inhomogeneous boundary condition. The study assumes the approximation of the original problem by Galerkin-type approximations followed by a passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a non-smooth velocity field.
About the authors
V. G. Zvyagin
Voronezh State University
Author for correspondence.
Email: vsu@mail.ru
Russian Federation, Voronezh
V. P. Orlov
Voronezh State University
Author for correspondence.
Email: vp@mail.ru
Russian Federation, Voronezh
References
- Осколков А.П. Начально-краевые задачи для уравнений движения жидкостей Кельвина–Фойгта и жидкостей Олдройта // Тр. МИАН СССР. 1988. Т. 179. С. 126–164.
- Zvyagin V.G., Vorotnikov D.A. Topological approximation methods for evolutionary problems of nonlinear hydrodynamics. de Gruyter Series in Nonlinear Analysis and Applications. V. 12. Berlin: Walter de Gruyter & Co, 2008. 230 p.
- Звягин В.Г., Орлов В.П. О слабой разрешимости задачи вязкоупругости с памятью // Дифференц. уравнения. 2017. Т. 53. № 2. С. 215–220.
- Zvyagin V.G., Orlov V.P. Solvability of one non-Newtonian fluid dynamics model with memory // Nonlinear Analysis: TMA. 2018. V. 172. P. 73–98.
- Zvyagin V.G., Orlov V.P. Weak solvability of fractional Voigt model of viscoelasticity // Discrete and Continuous Dynamical Systems, Series A. 2018. V. 38. № 12. P. 6327–6350.
- Zvyagin V.G., Orlov V.P. On one problem of viscoelastic fluid dynamics with memory on an infinite time interval // Discrete and Continuous Dynamical Systems, Series B. 2018. V. 23. № 9. P. 3855–3877.
- Коробков М.В., Пилецкас К., Пухначёв В.В., Руссо Р. Задача протекания для уравнений Навье–Стокса // УМН. 2014. Т. 69. № 6. С. 115–176.
- Ладыженская О.А., Солонников В.А. О некоторых задачах векторного анализа и обобщенных постановках краевых задач для уравнений Навье–Стокса // Зап. научн. сем. ЛОМИ. 1976. Т. 59. С. 81–116.
- Ворович И.И., Юдович В.И. Стационарное течение вязкой несжимаемой жидкости // Матем. сб. 1961. Т. 53. № 4. С. 393–428.
- Avrin J. Existence, uniqueness, and asymptotic stability results for the 3- steady and unsteady Navier–Stokes equations on multi-connected domains with inhomogeneous boundary conditions // Asymptotic Analysis. 2022. V. Pre-press. № Pre-press. pp. 1–22, 2022. https://doi.org/10.3233/ASY-22181610.3233/ASY-221816
- Avrin J. The 3- Spectrally-Hyperviscous Navier-Stokes Equations on Bounded Domains with Zero Boundary Conditions // arXiv:1908.11005v1 [math.AP] 29 Aug 2019.
- Ворович И.И., Юдович В.И. Стационарное течение вязкой несжимаемой жидкости // Матем. сб. 1961. Т. 53. № 4. С. 393–428.
- Темам Р. Уравнения Навье–Стокса. Теория и численный анализ. М: Мир, 1987. 408 с.
- DiPerna R.J., Lions P.L. Ordinary differential equations, transport theory and Sobolev spaces // Invent. Math. V. 1989. 98. P. 511–547.
- Crippa G., de Lellis C. Estimates and regularity results for the diPerna–Lions flow // J. Reine Angew. Math. 2008. V. 616. P. 15–46.
- Ладыженская О.А. Математические вопросы динамики вязкой несжимаемой жидкости. М: Наука, 1970. 204 с.
Supplementary files
