Geodesic
Attractors for an autonomous model of the motion of a nonlinear viscous fluid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 74-91.

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In this paper, we examine the limit behavior of weak solutions of an autonomous model of motions of a nonlinear viscous fluid, 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.
Keywords: attractor, trajectory space, nonlinear viscous fluid, weak solution. 
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V. G. Zvyagin; M. V. Kaznacheev. Attractors for an autonomous model of the motion of a nonlinear viscous fluid. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 74-91. http://geodesic.mathdoc.fr/item/INTO_2021_191_a6/

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