Strongly compact strong trajectory attractors for evolutionary systems and their applications

We show that for any fixed accuracy and time length T, a finite number of T-time pieces the complete trajectories on global attractor are capable uniformly approximating all within in natural strong metric after sufficiently large when observed dissipative system is asymptotically compact. Moreover, we obtain equicontinuity attractor. These results follow by proving existence strongly compact trajectory The notion was previously constructed family auxiliary systems including originally considered one without uniqueness. Recently, Cheskidov author developed new framework called evolutionary system, with which (weak) can be actually defined original system. In this paper, theory attractors further our purpose. then apply it to both 2D 3D Navier–Stokes equations general nonautonomous reaction–diffusion