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Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories

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  • Mikhail Turbin

    (Research Institute of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394018 Voronezh, Russia)

  • Anastasiia Ustiuzhaninova

    (Research Institute of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394018 Voronezh, Russia)

Abstract

This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved.

Suggested Citation

  • Mikhail Turbin & Anastasiia Ustiuzhaninova, 2024. "Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:266-:d:1318820
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    References listed on IDEAS

    as
    1. Mikhail V. Turbin, 2006. "Research of a mathematical model of low-concentrated aqueous polymer solutions," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-27, February.
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