Attractors of weak solutions to the regularized system of equations of motion of fluid media with memory
Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1611-1630 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of a trajectory attractor and a global attractor is established for weak solutions to the regularized model of the motion of fluid media with memory. Bibliography: 14 titles.
Keywords: regularized model of the motion of fluid media with memory, weak solutions, trajectory attractor, global attractor, existence theorems.
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V. G. Zvyagin; S. K. Kondrat'ev. Attractors of weak solutions to the regularized system of equations of motion of fluid media with memory. Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1611-1630. http://geodesic.mathdoc.fr/item/SM_2012_203_11_a4/

[1] V. T. Dmitrienko, V. G. Zvyagin, “Konstruktsii operatora regulyarizatsii v modelyakh dvizheniya vyazkouprugikh sred”, Vestn. VoronezhGU. Ser. 1. Matem., fiz., 2 (2004), 148–153 | Zbl

[2] V. G. Litvinov, “Regular model and nonstationary problem for the nonlinear viscoelastic fluid”, Siberian J. Differential Equations, 1:4 (1997), 351–382 | MR

[3] R. Temam, Navier–Stokes equations, Stud. Math. Appl., 2, North-Holland, Amsterdam–New York, 1979 | MR | MR | Zbl | Zbl

[4] V. G. Zvyagin, V. T. Dmitrienko, “On weak solutions of an initial-boundary value problem for the equation of motion of a viscoelastic fluid”, Dokl. Math., 64:2 (2001), 190–193 | MR | Zbl

[5] V. G. Zvyagin, V. T. Dmitrienko, “On weak solutions of a regularized model of a viscoelastic fluid”, Differ. Equ., 38:12 (2002), 1731–1744 | DOI | MR | Zbl

[6] V. G. Zvyagin, D. A. Vorotnikov, Topological approximation methods for evolutionary problems of nonlinear hydrodynamics, De Gruyter Ser. Nonlinear Anal. Appl., 12, de Gruyter, Berlin, 2008 | MR | Zbl

[7] V. V. Chepyzhov, M. I. Vishik, “Trajectory attractors for evolution equations”, C. R. Acad. Sci. Paris Sér. I Math., 321:10 (1995), 1309–1314 | DOI | MR | Zbl

[8] 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

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

[10] G. R. Sell, “Global attractors for the three-dimensional Navier–Stokes equations”, J. Dynam. Differential Equations, 8:1 (1996), 1–33 | DOI | MR | Zbl

[11] G. R. Sell, Y. You, Dynamics of evolutionary equations, Appl. Math. Sci., 143, Springer-Verlag, New York, 2002 | MR | Zbl

[12] M. I. Vishik, V. V. Chepyzhov, “Trajectory and global attractors of three-dimensional Navier–Stokes systems”, Math. Notes, 71:2 (2002), 177–193 | DOI | MR | Zbl

[13] D. A. Vorotnikov, V. G. Zvyagin, “Trajectory and global attractors of the boundary value problem for autonomous motion equations of viscoelastic medium”, J. Math. Fluid Mech., 10:1 (2008), 19–44 | DOI | MR | Zbl

[14] V. G. Zvyagin, V. T. Dmitrienko, Approksimatsionno-topologicheskii podkhod k issledovaniyu zadach gidrodinamiki. Sistema Nave–Stoksa, Editorial URSS, M., 2004