В., доктор физико-математических наук, профессор, заведующий кафедрой высшей математики, Воронежский государственный педагогический университет, Воронеж, Российская Федерация E-mail: valerio-ob2000@mail.ru Тел.: 255–36–63 Obukhovskii V., Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia E-mail: valerio-ob2000@mail.ru Tel.: 255–36–63 ВЕСТНИК ВГУ. <...> МАТЕМАТИКА. 2014. № 3 99 UDK 517.9 REVIEW OF ATTRACTORS FOR A MODEL OF MOTION OF WEAK AQUEOUS POLYMER SOLUTIONS V. G. Zvyagin, S. K. Kondratyev (Research Institute of Mathematics, Voronezh State University) Поступила в редакцию 22.03.2014 г. <...> Abstract: the aim of this paper is to demonstrate how the approximating topological method can be effectively combined with the theory of attractors of trajectory spaces in problems of fluid mechanics. <...> We consider the model of motion of weak aqueous polymer solutions and prove that it has the minimal trajectory attractor and the global one. <...> Then we prove that the attractors of approximating problem converge to the attractors of the unperturbed one. <...> Key words and phrases: Non-Newtonian fluids, approximating topological method, trajectory space, trajectory attractor, global attractor, convergence of attractors. <...> Ключевые слова: неньютонова жидкость, аппроксимационно-топологический метод, траекторные пространства, траекторный аттрактор, глобальный аттрактор, сходимость аттракторов. 1. <...> EQUATIONS OF MOTION We illustrate the application of the approximating topological approach to problems of fluid mechanics with the autonomous initial boundary problem for the mathematical model of motion of weak aqueous polymer solutions. <...> МАТЕМАТИКА. 2014. № 3 Review of attractors for a model of motion of weak aqueous polymer solutions boundary problem Let Ω ⊂ Rn be a bounded domain with a smooth boundary (n = 2, 3). <...> Equation (1.1) coresponds to the constitutive law σ = 2ν ( dt E +κν−1dE) , which establishes a relation between the deviator of the rate-of-strain tensor σ and the strain velocity tensor E. This constitutive law was suggested in [1] on the basis of research [2]. <...> On the contrary, the function a defining the initial condition (1.4) can be arbitrarily chosen in a functional space. <...> In the case of this problem neither the global solvability in the strong sense nor the uniqueness of the weak solution have been proved. <...> FUNCTIONAL SPACES <...>