Thomas Alazard (ENS Paris-Saclay)

The Analysis and PDE Seminar will take place on Monday, April 17, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Control of water waves

Abstract: Water waves are disturbances of the free surface of a liquid. They are, in general, produced by the immersion of a solid body or by impulsive pressures applied on the free surface. The question we discuss in this talk is the following: which waves can be generated by blowing on a localized portion of the free surface. Our main result asserts that one can generate any small amplitude, periodic in x, two-dimensional, gravity-capillary water waves. This is a result from control theory. More precisely, we prove the local exact controllability of the incompressible Euler equation with free surface. This is a joint work with Pietro Baldi and Daniel Han-Kwan.