Approximate controllability for 2D Euler equations

Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is relaxed when compared to previous literature, still being a sufficient condition for approximate controllability. The result holds for general bounded two-dimensional spatial domains with smooth boundary. An example of a saturating set is given in the case the spatial domain is the unit disk.