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.

中文翻译：

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非线性粘性流体自治模型的吸引子

对于非线性粘性流体运动的自主模型，我们研究了其弱解随着时间趋于无穷大的极限行为。即建立正半轴弱解的存在性，确定该模型解对应的轨迹空间，证明存在最小轨迹吸引子，进而证明相空间中存在全局吸引子使用轨迹空间理论。因此，事实证明，无论描述模型的系统的初始状态是什么，它都会随着时间被“遗忘”，并且会无限接近全局吸引子。