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<p>In this paper, we examine the limit behavior of weak solutions of an autonomous model of motions of a nonlinear viscous liquid in the case where the time tends to infinity. Namely, for solutions of the model considered, the existence of weak solutions on the positive semiaxis is proved, the corresponding trajectory space the model is introduced, and the existence of the minimal trajectory attractor and the global attractor in the phase space is proved. Thus, it turns out that any initial state of the system approaches to the global attractor.</p>

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Attractors for an Autonomous Model of the Motion of a Nonlinearly Viscous Liquid

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • V. G. Zvyagin,
  • M. V. Kaznacheev

摘要

In this paper, we examine the limit behavior of weak solutions of an autonomous model of motions of a nonlinear viscous liquid in the case where the time tends to infinity. Namely, for solutions of the model considered, the existence of weak solutions on the positive semiaxis is proved, the corresponding trajectory space the model is introduced, and the existence of the minimal trajectory attractor and the global attractor in the phase space is proved. Thus, it turns out that any initial state of the system approaches to the global attractor.