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 -------------------------------------------- *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. *