Initial–Boundary Value Problem for Flows of a Fluid with Memory in a 3D Network-Like Domain

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We consider an initial–boundary value problem for an integro-differential system that describes 3D flows of a non-Newtonian fluid with memory in a network-like domain. The problem statement uses the Dirichlet boundary conditions for the velocity and pressure fields as well as Kirchhoff-type transmission conditions at the internal nodes of the network. A theorem on the existence and uniqueness of a time-continuous weak solution is proved. In addition, an energy equality for this solution is derived.

作者简介

E. Baranovskiy

Voronezh State University, Voronezh, 394018, Russia

编辑信件的主要联系方式.
Email: esbaranovskii@gmail.com
Воронеж, Россия

参考

  1. Panasenko G., Pileckas K. Flows in a tube structure: equation on the graph // J. of Math. Phys. 2014. V. 55. Art. ID 081505.
  2. Provotorov V.V., Provotorova E.N. Optimal control of the linearized Navier-Stokes system in a netlike domain // Вестн. Санкт-Петербургского ун-та. Прикл. математика. Информатика. Процессы управления. 2017. Т. 13. № 4. C. 431-443.
  3. Baranovskii E.S., Provotorov V.V., Artemov M.A., Zhabko A.P. Non-isothermal creeping flows in a pipeline network: existence results // Symmetry. 2021. V. 13. № 7. Art. ID 1300.
  4. Astarita G., Marucci G. Principles of Non-Newtonian Fluid Mechanics. New York, 1974.
  5. Cioranescu D., Girault V., Rajagopal K.R. Mechanics and Mathematics of Fluids of the Differential Type. Cham, 2016.
  6. Брутян М.А., Крапивский П.Л. Гидродинамика неньютоновских жидкостей // Итоги науки и техники. Сер. Комплексные и специальные разделы механики. 1991. Т. 4. С. 3-98.
  7. Saut J.-C. Lectures on the mathematical theory of viscoelastic fluids // Lect. on the Analysis of Nonlinear Partial Differential Equations. Part 3. Somerville, 2013. P. 325-393.
  8. Baranovskii E.S. A novel 3D model for non-Newtonian fluid flows in a pipe network // Math. Methods in the Appl. Sci. 2021. V. 44. № 5. P. 3827-3839.
  9. Рагулин В.В. К задаче о протекании вязкой жидкости сквозь ограниченную область при заданном перепаде давления и напора // Динамика сплошной среды. 1976. Т. 27. C. 78-92.
  10. Oskolkov A.P., Shadiev R. Towards a theory of global solvability on $[0,infty)$ of initial-boundary value problems for the equations of motion of Oldroyd and Kelvin-Voight fluids // J. of Math. Sci. 1994. V. 68. P. 240-253.
  11. Oskolkov A.P. Smooth global solutions of initial boundary-value problems for the equations of Oldroyd fluids and of their $epsilon $-approximations // J. of Math. Sci. 1998. V. 89. P. 1750-1763.
  12. Bir B., Goswami D. On a three step two-grid finite element method for the Oldroyd model of order one // ZAMM Zeitschrift f"ur Angewandte Mathematik und Mechanik. 2021. Bd. 101. № 11. Art. ID e202000373.
  13. Beir ao da Veiga H. On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip and non-slip boundary conditions // Comm. Pure Appl. Math. 2005. V. 58. P. 552-577.
  14. Baranovskii E.S., Artemov M.A. Global existence results for Oldroyd fluids with wall slip // Acta Applicandae Mathematicae. 2017. V. 147. № 1. P. 197-210.
  15. Baranovskii E.S. Steady flows of an Oldroyd fluid with threshold slip // Comm. on Pure and Appl. Anal. 2019. V. 18. № 2. P. 735-750.
  16. Galdi G.P. An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Steady-State Problems. New York, 2011.
  17. Temam R. Navier-Stokes Equations. Theory and Numerical Analysis. Amsterdam; New York; Oxford, 1977.
  18. Nev{c}as J. Direct Methods in the Theory of Elliptic Equations. Heidelberg, 2012.

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