Abstract
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical studies of periodic waves with critical layers that may overhang; existence, nonexistence, and qualitative theory of solitary waves and fronts; traveling waves with localized vorticity or density stratification; and waves in three dimensions.
Original language | English |
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Pages (from-to) | 317-401 |
Number of pages | 85 |
Journal | Quarterly of Applied Mathematics |
Volume | 80 |
Issue number | 2 |
Early online date | 14 Mar 2022 |
DOIs | |
Publication status | Published - 30 Jun 2022 |
Bibliographical note
Funding Information:Received September 30, 2021, and, in revised form, January 5, 2022. 2020 Mathematics Subject Classification. Primary 35Q35, 35Q31, 76B15, 76B25, 76B47. The work of the first author was partially funded by the Austrian Science Fund (FWF), Grant Z 387-N. The work of the second author was partially funded by the NSF through the award DMS-2009981. The work of the third author was partially funded by the NSF through the award DMS-1812436. The work of the fourth author was partially funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 678698) and the Swedish Research Council (grant nos. 621-2012-3753 and 2016-04999).
ASJC Scopus subject areas
- Applied Mathematics