Attractor of the limiting Navier--Stokes--Voigt system in ${\mathbb{R}}^4$

The Navier–Stokes–Voigt system in the whole four-dimensional space is considered. Although we do not know any physical reasons to consider this system in space dimension four, the attractors theory for this case becomes especially simple and elegant and nothing similar happens when the space dimension is different than four. These notes are devoted to developing this theory, including well-posedness, dissipativity, existence of a global attractor and estimates for its dimension.