Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Traveling water waves — the ebb and flow of two centuries


Authors: Susanna V. Haziot, Vera Mikyoung Hur, Walter A. Strauss, J. F. Toland, Erik Wahlén, Samuel Walsh and Miles H. Wheeler
Journal: Quart. Appl. Math. 80 (2022), 317-401
MSC (2020): Primary 35Q35, 35Q31, 76B15, 76B25, 76B47
DOI: https://doi.org/10.1090/qam/1614
Published electronically: March 14, 2022
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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.


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Additional Information

Susanna V. Haziot
Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
MR Author ID: 1235461
ORCID: 0000-0001-5156-8809
Email: susanna.haziot@univie.ac.at

Vera Mikyoung Hur
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
MR Author ID: 782185
ORCID: 0000-0003-1563-3102
Email: verahur@math.uiuc.edu

Walter A. Strauss
Affiliation: Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island 02912
MR Author ID: 168085
Email: walter_strauss@brown.edu

J. F. Toland
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
MR Author ID: 173135
ORCID: 0000-0002-6551-0998
Email: masjft@bath.ac.uk

Erik Wahlén
Affiliation: Centre for Mathematical Sciences, Lund University, P.O. Box 118, 22100 Lund, Sweden
ORCID: 0000-0002-9495-0642
Email: erik.wahlen@math.lu.se

Samuel Walsh
Affiliation: Department of Mathematics, University of Missouri, 202 Math Sciences Building, Columbia, Missouri 65211
MR Author ID: 878234
Email: walshsa@missouri.edu

Miles H. Wheeler
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
MR Author ID: 920346
ORCID: 0000-0002-7286-9587
Email: mw2319@bath.ac.uk

Received by editor(s): September 30, 2021
Received by editor(s) in revised form: January 5, 2022
Published electronically: March 14, 2022
Additional Notes: 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)
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