THE PROBLEM OF THE FLOW OF ONE TYPE OF NON-NEWTONIAN FLUID THROUGH THE BOUNDARY OF A MULTI-CONNECTED DOMAIN

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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.

Sobre autores

V. Zvyagin

Voronezh State University

Autor responsável pela correspondência
Email: vsu@mail.ru
Russian Federation, Voronezh

V. Orlov

Voronezh State University

Autor responsável pela correspondência
Email: vp@mail.ru
Russian Federation, Voronezh

Bibliografia

  1. Осколков А.П. Начально-краевые задачи для уравнений движения жидкостей Кельвина–Фойгта и жидкостей Олдройта // Тр. МИАН СССР. 1988. Т. 179. С. 126–164.
  2. 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.
  3. Звягин В.Г., Орлов В.П. О слабой разрешимости задачи вязкоупругости с памятью // Дифференц. уравнения. 2017. Т. 53. № 2. С. 215–220.
  4. 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.
  5. 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.
  6. 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.
  7. Коробков М.В., Пилецкас К., Пухначёв В.В., Руссо Р. Задача протекания для уравнений Навье–Стокса // УМН. 2014. Т. 69. № 6. С. 115–176.
  8. 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.
  9. Ворович И.И., Юдович В.И. Стационарное течение вязкой несжимаемой жидкости // Матем. сб. 1961. Т. 53. № 4. С. 393–428.
  10. 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
  11. Avrin J. The 3- Spectrally-Hyperviscous Navier-Stokes Equations on Bounded Domains with Zero Boundary Conditions // arXiv:1908.11005v1 [math.AP] 29 Aug 2019.
  12. Ворович И.И., Юдович В.И. Стационарное течение вязкой несжимаемой жидкости // Матем. сб. 1961. Т. 53. № 4. С. 393–428.
  13. Темам Р. Уравнения Навье–Стокса. Теория и численный анализ. М: Мир, 1987. 408 с.
  14. DiPerna R.J., Lions P.L. Ordinary differential equations, transport theory and Sobolev spaces // Invent. Math. V. 1989. 98. P. 511–547.
  15. Crippa G., de Lellis C. Estimates and regularity results for the diPerna–Lions flow // J. Reine Angew. Math. 2008. V. 616. P. 15–46.
  16. Ладыженская О.А. Математические вопросы динамики вязкой несжимаемой жидкости. М: Наука, 1970. 204 с.

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