# Mathematical Sciences Research Institute

Home » Water waves and other interface problems (Part 1): Control of 3D gravity-capillary water waves

# Seminar

Water waves and other interface problems (Part 1): Control of 3D gravity-capillary water waves February 23, 2021 (08:00 AM PST - 09:00 AM PST)
Parent Program: Mathematical problems in fluid dynamics MSRI: Online/Virtual
Speaker(s) Hui Zhu (University of Michigan)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Video

#### Control of 3D Gravity-Capillary Water Waves

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

I will present a result on the controllability of the gravity-capillary water wave system with arbitrary spatial dimensions. I will prove that, if $\omega$ is a domain of the free surface satisfying a geometric control condition, then by applying an exterior pressure on $\omega$, we can generate arbitrary shapes of the free surface and arbitrary vector fields of the fluid provided they are both sufficiently small. This result generalizes the work of Alazard, Baldi and Han-Kwan on the controllability of the gravity-capillary water wave system with two spatial dimensions.