Geodesic
Attractors of an autonomous model of nonlinear viscous fluid
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 57-60.

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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.
Keywords: attractors, trajectory space, nonlinear viscous fluid. 
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V. G. Zvyagin; M. V. Kaznacheev. Attractors of an autonomous model of nonlinear viscous fluid. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 57-60. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a10/

[1] Chepyzhov V.V., Vishik M.I., Attractors for equations of mathematical physics, American Mathematical Society Colloquium Publications, 49, American Mathematical Society, Providence, 2002 | MR | Zbl

[2] Sell G.R., You Y., Dynamics of Evolutionary Equations, Springer, N.Y., 1998, 672 pp. | MR

[3] Vishik M.I., Chepyzhov V.V., Matem. zametki, 71:2 (2002), 194–213 | DOI | Zbl

[4] Vorotnikov D.A., Zvyagin V.G., J. Math. Fluid Mech., 10 (2008), 19–44 | DOI | MR | Zbl

[5] Vorotnikov D.A., Zvyagin V.G., J. Math. Anal. Appl., 325 (2007), 438–458 | DOI | MR | Zbl

[6] Zvyagin V.G., Kondratev S.K., Uspekhi mat. nauk, 69:5(419) (2014), 81–156 | DOI | MR | Zbl

[7] Zvyagin V.G., Vorotnikov D.A., Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics, Walter de Gruyter, B.–N.Y., 2008, 243 pp. | MR

[8] Litvinov V.G., Dvizhenie nelineino-vyazkoi zhidkosti, Nauka, M., 1982, 376 pp. | MR

[9] Sobolevskii P.E., DAN SSSR, 285:1 (1985), 44–48 | MR | Zbl

[10] Dmitrienko V.T., Zvyagin V.G., Abstract and Applied Analysis, 2:1 (1997), 1–45 | DOI | MR | Zbl