This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations....

L'autore dà una condizione necessaria e sufficiente per la risolubilità formale degli operatori differenziali a coefficienti costanti, lineari, $p\left(D\right)$, in termini di prolungamento, come distribuzioni, delle $u\in D^{\prime }\left({\mathbb{R}}^n-\left\{0\right\}\right)$, tali che $p\left(-D\right)u=0$.