anche se è già apparso sul notiziario del dipartimento, segnalo il seminario di domani di Riccardo Montalto.
TITOLO: Construction on quasi-periodic nonlinear waves in fluid mechanics
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 permittiing) 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