Local exact boundary controllability of 3D Navier–Stokes equations

Given a time-dependent solution of the Navier–Stokes equations and an arbitrary open subset of the boundary, the existence of a boundary control, supported in the given subset, that drives the system to the given solution in finite time is proven.Null controllability of the Oseen system is investigated as well, and continuity results of the driving control on the initial data are derived.