ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 2 РАЗДЕЛ МАТЕМАТИКА УДК 517.9+612.3.06 INVESTIGATIONS OF PROPERTIES OF ATTRACTORS FOR A REGULARIZED MODEL OF THE MOTION OF A NONLINEAR-VISCOUS FLUID © 2001 г. <...> Agranovich, Viktor G. Zvyagin Voronezh State Technical University, Voronezh State University 1. <...> The phenomenological description of the flow of such fluids has been the object of consideration of mechanicians during the last sixty years. <...> The survey of suggested models and of their rheological properties can be found, for example, in the known monograph G. Astarita and G. Marrucci [3] and in the fundamental work C. Truesdell and W. Noll [15]. <...> Here, as well as for Navier-Stokes equations, the problem of proving the solvability of the Cauchy problem on an arbitrary time interval arises in a strong form. <...> For the mathematical investigation of models of nonlinear-viscous fluids from [11] a D -approximation was used for inertia terms Dv ≥= =∑ 2 () n = 0, vv n , 2,3, i=1 1 + 2 v v 2 i grad v, (1) suggested by P. E. Sobolevskii in [12] was applied, where it was proved that the equations of the motion of nonlinear-viscous fluid, regularized in such way, have for > 0 unique strong solution on any finite time segment, both in the cases of two and three space variables. <...> The last in turn, means that we have reason to study 50 the minimal global attractor of the given system, i.e. set M is equal intersection the sets Vt t ≥ 0, where X is a phase space and Vt (X), is some group Vt, t ∈ ¡. <...> The estimates proved in what follows show that the quantity semigroup with operators for the evolutionary problem. <...> We will call minimal global B-attractor for a semigroup a minimal nonempty closed set in X, that attracting any bounded subset B in X. But, in our sense attractor is some subset in phase space on that a semigroup Vt expand to a , which we will call later on the inertia parameter, plays for the attractor the same role as the viscosity of the fluid. <...> We explain it more in detail: D (v) can be represented in the form: =+ Ч Dv 2 grad[ln(1)] − v =0 ( 1 + therefore (D <...>