On the Weak Solvability of High-order Viscoelastic Fluid Dynamics Model

A model of a viscoelastic fluid with a high-order rheological relation and a memory along the trajectories of the velocity field is under consideration. The weak solvability to the corresponding initial-boundary value problem is established. The investigation is based on the approximation of the pro...

Full description

Saved in:
Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 4; pp. 1524 - 1543
Main Authors Zvyagin, V. G., Zvyagin, A. V., Orlov, V. P., Turbin, M. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2024
Springer Nature B.V
Subjects
Algebra
Analysis
Boundary value problems
Fluid dynamics
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Rheological properties
Velocity distribution
Viscoelastic fluids
weak solution
viscoelastic fluid
regular Lagrangian flow
high-order fluid
a priori estimate
existence theorem
Online AccessGet full text

Cover

More Information
Summary:A model of a viscoelastic fluid with a high-order rheological relation and a memory along the trajectories of the velocity field is under consideration. The weak solvability to the corresponding initial-boundary value problem is established. The investigation is based on the approximation of the problem under consideration by a sequence of regularized problems, and the following passage to the limit. The theory of regular Lagrangian flows is used to study trajectories of a non-smooth velocity fields.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224601279