In this talk I will discuss some recent results on Euler and Navier-Stokes equations concerning the construction of quasi-periodic solutions and the problem of the invscid limit for the Navier-Stokes equation. I will discuss the following two results:
1) Construction of quasi-periodic solutions for the Euler equation with a time quasi-periodic external force, bifurcating from a constant, diophantine velocity field;
2) I shall discuss the inviscid limit problem from the perspective of KAM theory, namely I shall prove the existence of quasi-periodic solutions of the Navier Stokes equation converging to the one of the Euler equation constructed in 1).
The main difficulty is that this is a singular limit problem. We overcome this difficulty by implementing a normal form methods which allow to prove sharp estimates (global in time) with respect to the viscosity parameter.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
