Analysis and controllability of Partial Differential Equations

We investigate some partial differential equations, in particular, in connection with fluid mechanics, including climate models and fluid-structure interactions, as well as magnetohydrodynamics and micro-magnetism. On the top of the existence and uniqueness of solutions to these equations, we explore some qualitative and asymptotic properties, with a special emphasis on the multi-scale phenomena which occur for such systems. We also look for some strategies to control them by the means of appropriate external actions.