One of the main big questions in Fluid Dynamics is the behaviour of weakly viscous fluids and their relations with inviscid ones. In my talk I will present is to present a recent result where quasi-periodic solutions for the forced 2D Navier-Stokes equation are constructed so that they converge to quasi-periodic solutions of the 2D Euler equations in the vanishing viscosity limit. Compared to previous results in literature, this is the first example where the zero viscosity limit is proved to hold for all times.
I will introduce the problem and a bit of the history so far. Then, after stated the main result, I will present the main ideas to construct such solutions. In particular, it relies on a good knowledge of the linearized Euler equation, on its reversibility nature and on a normal form argument to overcome the singular limit issue. This is a joint work with Riccardo Montalto (University of Milan).