Traveling water waves — the ebb and flow of two centuries

Susanna Haziot; Vera Hur; Walter A. Strauss; John Toland; Erik Wahlén; Samuel Walsh; Miles Wheeler

doi:10.1090/qam/1614

Traveling water waves — the ebb and flow of two centuries

Susanna Haziot
, Vera Hur
, Walter A. Strauss
, John Toland
, Erik Wahlén
, Samuel Walsh
, Miles Wheeler

Department of Mathematical Sciences

University of Vienna
University of Illinois at Urbana-Champaign
Brown University
Lund University
University of Missouri-Columbia

Research output: Contribution to journal › Article › peer-review

47 Citations (SciVal)

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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.

Original language	English
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	https://doi.org/10.1090/qam/1614
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

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10.1090/qam/1614

arXiv preprint.PDFAccepted author manuscript, 3.08 MB

Cite this

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title = "Traveling water waves — the ebb and flow of two centuries",

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. ",

author = "Susanna Haziot and Vera Hur and Strauss, \{Walter A.\} and John Toland and Erik Wahl{\'e}n and Samuel Walsh and Miles Wheeler",

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{\textquoteright}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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doi = "10.1090/qam/1614",

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AU - Haziot, Susanna

AU - Hur, Vera

AU - Strauss, Walter A.

AU - Toland, John

AU - Wahlén, Erik

AU - Walsh, Samuel

AU - Wheeler, Miles

N1 - 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).

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AB - 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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Traveling water waves — the ebb and flow of two centuries

Abstract

Bibliographical note

ASJC Scopus subject areas

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