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Attractors of an Autonomous Model of Nonlinear Viscous Fluid

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Abstract

For an autonomous model of the motion of a nonlinear viscous fluid, we study the limiting behavior of its weak solutions as time tends to infinity. Namely, the existence of weak solutions on the positive half-axis is established, the trajectory space corresponding to the solutions of this model is determined, and the existence of a minimum trajectory attractor and, then, a global attractor in the phase space is proved using the theory of trajectory spaces. Thus, it turns out that whatever the initial state of the system describing the model is, it is “forgotten” over time and the global attractor is infinitely approached.

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Funding

This work was supported by the Russian Science Foundation, project no. 19-11-00146.

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Authors and Affiliations

  1. Voronezh State University, 394018, Voronezh, Russia

    V. G. Zvyagin & M. V. Kaznacheev

Authors
  1. V. G. Zvyagin
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  2. M. V. Kaznacheev
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Corresponding authors

Correspondence to V. G. Zvyagin or M. V. Kaznacheev.

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Translated by I. Ruzanova

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Zvyagin, V.G., Kaznacheev, M.V. Attractors of an Autonomous Model of Nonlinear Viscous Fluid. Dokl. Math. 101, 126–128 (2020). https://doi.org/10.1134/S1064562420020271

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  • DOI: https://doi.org/10.1134/S1064562420020271

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