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

Mikhail Turbin () and Anastasiia Ustiuzhaninova
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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

Mathematics, 2024, vol. 12, issue 2, 1-27

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.

Keywords: trajectory attractor; global attractor; Kelvin–Voigt model; regular Lagrangian flow; boundary value problem; non-Newtonian fluid; a priory estimate; existence theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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