Monday, February 5, 2018 - 10:10
1 hour (actually 50 minutes)
In this talk I will present some results concerning the existence and the stability of quasi-periodic solutions for quasi-linear and fully nonlinear PDEs. In particular, I will focus on the Water waves equation. The proof is based on a Nash-moser iterative scheme and on the reduction to constant coefficients of the linearized PDE at any approximate solution. Due to the non-local nature of the water waves equation, such a reduction procedure is achieved by using techniques from Harmonic Analysis and microlocal analysis, like Fourier integral operators and Pseudo differential operators.