TRAJECTORY ATTRACTORS FOR EVOLUTION-EQUAT IONS

We study the global trajectory attractors existence and structure prob lems for nonautonomous evolution equations. We do not suppose the uniq ue solvability of the corresponding Cauchy problem. We present the gen eral attractor construction scheme for operator evolution equations an d we prove the theorem on the existence, the structure, and the approx imation from below of the attractors. In applications we consider: 1) non-autonomous dissipative hyperbolic equation having an arbitrary gro wth of the nonlinear term; 2) 3D Navier-Stokes system with the transla tion bounded in L(2)(loc) (R(+), V') [see (11)] external force; 3) the non-autonomous reaction-diffusion system without uniqueness. All the mentioned above theorems are also applicable to equations for which th e uniqueness theorem take place.