Attractor of the Limit Navier–Stokes–Voigt System in R⁴

The Navier–Stokes–Voigt system on the entire four-dimensional space R⁴ is considered. Although we do not know any physical reason to consider this system in the four-dimensional space, the attractors theory for this case becomes especially simple and elegant and nothing similar happens when the space dimension is not four. In the present note, we develop this theory, including well-posedness, dissipativity, existence of a global attractor, and estimates for its dimension.