Logo

Mathematical Sciences Research Institute

Home » Water waves and other interface problems (Part 2): Smooth stationary water waves with exponentially localised vorticity

Seminar

Water waves and other interface problems (Part 2): Smooth stationary water waves with exponentially localised vorticity April 06, 2021 (09:30 AM PDT - 10:30 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Mats Ehrnstrom (Norwegian University of Science and Technology (NTNU))
Description

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

Video

Smooth Stationary Water Waves with Exponentially Localised Vorticity

Abstract/Media

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

We construct small-amplitude surface water waves travelling over a large but finite depth in a fluid with concentrated vorticity. The construction is based on a bifurcation-like argument, although one where the bifurcation is rather done from something that is not a water wave solution per se, but a radial and exponentially decaying ground state of a semi-linear elliptic problem in the whole plane.

The proof consists of several parts, where some precise reflection estimates at the surface and flat bed play a major role, as does the fact that everything is exponentially decaying away from the concentrated vorticity. Finally, the vertical replacement of the centre of vorticity with respect to the surface and flat bed is necessary to guarantee a travelling solitary wave whose motion is governed by the very concentrated, but everywhere present, vorticity.

This is joint work with C. Zeng (Georgia Tech) and S. Walsh (Missouri).

Asset no preview Notes 3.09 MB application/pdf
Asset no preview Notes 2 160 KB application/pdf

Smooth Stationary Water Waves with Exponentially Localised Vorticity