Geodesic
Pullback attractors for the model of motion of dilute aqueous polymer solutions
Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 645-667.

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We study the qualitative dynamics of weak solutions in the non-autonomous model of motion of dilute aqueous polymer solutions using the theory of pullback attractors of trajectory spaces. We establish the existence of weak solutions for this model, define a family of trajectory spaces, introduce the notions of a trajectory pullback attractor and a minimal pullback attractor and prove the existence of these attractors.
Keywords: pullback attractors, trajectory space, weak solutions, existence theorems.
Mots-clés : dilute aqueous polymer solutions 
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V. G. Zvyagin; S. K. Kondrat'ev. Pullback attractors for the model of motion of dilute aqueous polymer solutions. Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 645-667. http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a0/

[1] A. N. Carvalho, J. A. Langa, J. C. Robinson, Attractors for infinite-dimensional non-autonomous dynamical systems, Appl. Math. Sci., 182, Springer, New York, 2013, xxxvi+409 pp. | DOI | MR | Zbl

[2] D. Vorotnikov, “Asymptotic behaviour of the non-autonomous 3D Navier–Stokes problem with coercive force”, J. Differential Equations, 251:8 (2011), 2209–2225 | DOI | MR | Zbl

[3] V. V. Chepyzhov, M. I. Vishik, “Evolution equations and their trajectory attractors”, J. Math. Pures Appl. (9), 76:10 (1997), 913–964 | DOI | MR | Zbl

[4] V. V. Chepyzhov, M. I. Vishik, Attractors for equations of mathematical physics, Amer. Math. Soc. Colloq. Publ., 49, Amer. Math. Soc., Providence, RI, 2002, xii+363 pp. | MR | Zbl

[5] V. G. Zvyagin, D. A. Vorotnikov, Topological approximation methods for evolutionary problems of nonlinear hydrodynamics, De Gruyter Ser. Nonlinear Anal. Appl., 12, Walter de Gruyter Co., Berlin, 2008, xii+230 pp. | DOI | MR | Zbl

[6] V. G. Zvyagin, S. K. Kondrat'ev, “Attractors of equations of non-Newtonian fluid dynamics”, Russian Math. Surveys, 69:5 (2014), 845–913 | DOI | DOI

[7] V. A. Pavlovskii, “K voprosu o teoreticheskom opisanii slabykh vodnykh rastvorov polimerov”, Dokl. AN SSSR, 200:4 (1971), 809–812

[8] V. B. Amfilokhiev, Ya. I. Voitkunskii, N. P. Mazaeva, Ya. S. Khodorkovskii, “Techeniya polimernykh rastvorov pri nalichii konvektivnykh uskorenii”, Tr. Leningr. korablestr. in-ta, 96, 1975, 3–9

[9] V. G. Zvyagin, M. V. Turbin, “The study of initial-boundary value problems for mathematical models of the motion of Kelvin–Voigt fluids”, J. Math. Sci. (N. Y.), 168:2 (2010), 157–308 | DOI | MR | Zbl

[10] V. G. Zvyagin, M. V. Turbin, Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, KRASAND, M., 2012, 416 pp.

[11] S. K. Kondratev, “Ob attraktorakh modeli dvizheniya slabokontsentrirovannykh vodnykh rastvorov polimerov”, Vestn. VGU. Ser. Fiz. Matem., 1 (2010), 117–138

[12] V. G. Zvyagin, S. K. Kondratyev, “Approximating topological approach to the existence of attractors in fluid mechanics”, J. Fixed Point Theory Appl., 13:2 (2013), 359–395 | DOI | MR | Zbl

[13] V. G. Zvyagin, S. K. Kondratyev, “Pullback attractors for a model of motion of weak aqueous polymer solutions”, Dokl. Math., 90:3 (2014), 660–662 | DOI | DOI | Zbl

[14] A. V. Fursikov, Optimal control of distributed systems. Theory and applications, Transl. Math. Monogr., 187, Amer. Math. Soc., Providence, RI, 2000, xiv+305 pp. | MR | Zbl | Zbl

[15] R. Temam, Navier–Stokes equations. Theory and numerical analysis, Stud. Math. Appl., 2, North-Holland Publishing Co., Amsterdam–New York, 1979, x+519 pp. | MR | MR | Zbl | Zbl