Weak global attractor for the 3D-Navier–Stokes equations via the globally modified Navier–Stokes equations

In this paper, we obtain the existence of a weak global attractor for the three-dimensional Navier–Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak topology, for initial data in bounded sets. To that end, we define this weak global attractor in terms of limits of solutions of the globally modified Navier–Stokes equations in the weak topology. We use the theory of semilinear parabolic equations and \(\epsilon \) $ϵ$ -regularity to obtain the local well-posedness for the globally modified Navier–Stokes equations, the existence of the global attractor and its regularity.