On Weak Solvability of a Flow Problem for Viscoelastic Fluid with Memory

Author:

Zvyagin V. G.1,Orlov V. P.1

Affiliation:

1. Voronezh State University

Abstract

The existence of weak solutions of the initial-boundary value problem for the equations of motion of a viscoelastic fluid with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is proved. The study relies on Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to examine the behavior of trajectories of a nonsmooth velocity field.

Publisher

The Russian Academy of Sciences

Reference17 articles.

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2. Звягин В.Г., Орлов В.П. О слабой разрешимости задачи вязкоупругости с памятью // Дифференц. ур‑ния. 2017. Т. 53. № 2. С. 215–220.

3. Zvyagin V.G., Orlov V.P. Solvability of one non-Newtonian fluid dynamics model with memory // Nonlin. Analys: TMA. 2018. V. 172. P. 73–98.

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5. Орлов В.П. Об одной неоднородной регуляризованной задаче динамики вязкоупругой среды // Изв. вузов. Матем. 2012. № 8. С. 58–64.

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