The energy of the incompressible Navier–Stokes equations is super-critical in two situations: the three-dimensional Cauchy problem and the two-dimensional steady-state problem. Both problems are difficult because the nonlinearity dominates the linearity, either locally (in the first case) or at large distances (in the second case). In this presentation, I will explain recent progress and conjectures about the steady-states of the Navier–Stokes equations in two-dimensional unbounded domains.