Abstract: The goal of this talk is to study the inviscid limit of a family $\omega^{\nu}$ of solutions of the 2D Navier-Stokes equations towards a renormalized/Lagrangian solution $\omega$ of the Euler equations. First I will prove the uniform-in-time $L^p$ convergence of $\omega^{\nu}$ towards $\omega$ in the setting of unbounded vorticities. This improves a recent result proved by Constantin-Drivas-Elgindi in the bounded case. Then I will show that it is also possible to obtain an explicit rate in the class of solutions with bounded vorticity. The proofs are based on the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations. In particular, the results are achieved by studying the zero-noise limit from stochastic towards deterministic flows of irregular vector fields.
Based on a joint work with G. Crippa (Universitaet Basel) and S. Spirito (Università degli Studi dell'Aquila).