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Quasi-periodic solutions and inviscid limit for Euler and Navier Stokes equations via KAM methods

Riccardo Montalto
Università di Milano
Thursday, May 4, 2023 - 11:00

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) w.r. to the viscosity parameter.

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