Friday, April 26, 2024 2pm to 3pm
About this Event
3620 South Vermont Avenue, Los Angeles, CA 90089
Luca Franzoi, University of Milan
Title: Quasi-periodic steady invariant structures in inviscid incompressible fluids
Abstract: Invariant structures and asymptotic behaviours close to shear flows are of great interest in Fluid Dynamics. In this talk, I present a recent result about the existence of nontrivial steady flows in the bounded channel that are quasi-periodic in the horizontal space direction and solve the incompressible Euler equation. Such solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction that may be resonant. This leads to a small divisor problem and the consequent loss of derivatives is overcome with a Nash-Moser nonlinear iteration. First, I recall the result of Lin and Zeng and their construction of space periodic flows. Then, I introduce the key ingredients in our setting and state the main result for space quasi-periodic flows. Finally, I show what the main issues in our strategy are and how to solve them. This is a joint work with Nader Masmoudi and Riccardo Montalto.