Smooth stationary water waves with exponentially localised vorticity

Geometric Aspects of Nonlinear Partial Differential Equations

15 November 15:00 - 16:00

Mats Ehrnström - NTNU - Norwegian University of Science and Technology

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).
Panagiota Daskalopoulos
Columbia University
Alessio Figalli
ETH Zürich
Erik Lindgren
Uppsala University
Henrik Shahgholian
KTH Royal Institute of Technology
Susanna Terracini,
University of Turin


Erik Lindgren

Henrik Shahgholian


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