The question of the stability for solutions of the Euler and the Navier-Stokes equations in the vanishing viscosity regime is one of the most important problems in fluid dynamics. The goal of this talk is to present a recent result where we construct a family of solutions of the forced 2D Navier-Stokes equation, bifurcating from given time quasi-periodic solutions of the incompressible 2D Euler equations and admitting vanishing viscosity limit to the latter. This limit holds uniformly for all times and independently of the size of the external forcing term. After the overview of the literature and the presentation of the main statement, I will give the main ideas for the construction of such solutions. In particular, our proof is based on the search of an approximate solution, up to an error of order $O(\nu^2)$, and the invertibility of the linearized Navier-Stokes operator at a quasi-periodic solution of the Euler equation. This is a joint work with Riccardo Montalto. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).