Dear Colleagues,
We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi:
Construction on quasi-periodic nonlinear waves in fluid mechanics,

Riccardo Montalto (Milano Statale).

The seminar will take place on TUE, 4.4.2023 at 13:30 CET in Sala Seminari, Dipartimento di Matematica, Pisa and streamed online at the link below.

Please notice that the seminar will take place half an hour earlier than usual.

The organizers,

A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco
https://sites.google.com/unipi.it/spass
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Abstract: 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 inviscid limit for the Navier Stokes equation. I will discuss the following 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;

3) (time permitting) I also discuss the construction of quasi-periodic traveling waves bifurcating from the Couette flow for the autonomous 2D Euler equation.

These works are based on collaborations with Luca Franzoi and Nader Masmoudi.