AMPLITUDE BOUNDS OF STEADY ROTATIONAL WATER WAVES

Susanna V. Haziot; Walter A. Strauss

doi:10.1137/24M1660565

AMPLITUDE BOUNDS OF STEADY ROTATIONAL WATER WAVES

Susanna V. Haziot
, Walter A. Strauss

Mathematics

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

Abstract

sssWe consider classical steady water waves with a free surface, a flat bottom, and constant vorticity Ɣ. In the adverse case Ɣ > 0 we prove the first absolute upper bound on the am-plitude, independent of the physical constants, provided that Ɣ is sufficiently small. In any favorable case Ɣ ≤ 0 we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as Ɣ tends to-∞.

Original language	English (US)
Pages (from-to)	1812-1830
Number of pages	19
Journal	SIAM Journal on Mathematical Analysis
Volume	58
Issue number	2
DOIs	https://doi.org/10.1137/24M1660565
State	Published - 2026

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

Keywords

amplitude
free boundary
vorticity
water waves

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10.1137/24M1660565

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title = "AMPLITUDE BOUNDS OF STEADY ROTATIONAL WATER WAVES",

abstract = "sssWe consider classical steady water waves with a free surface, a flat bottom, and constant vorticity Ɣ. In the adverse case Ɣ > 0 we prove the first absolute upper bound on the am-plitude, independent of the physical constants, provided that Ɣ is sufficiently small. In any favorable case Ɣ ≤ 0 we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as Ɣ tends to-∞.",

keywords = "amplitude, free boundary, vorticity, water waves",

author = "Haziot, \{Susanna V.\} and Strauss, \{Walter A.\}",

note = "Publisher Copyright: {\textcopyright} 2026.",

year = "2026",

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language = "English (US)",

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T1 - AMPLITUDE BOUNDS OF STEADY ROTATIONAL WATER WAVES

AU - Haziot, Susanna V.

AU - Strauss, Walter A.

PY - 2026

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N2 - sssWe consider classical steady water waves with a free surface, a flat bottom, and constant vorticity Ɣ. In the adverse case Ɣ > 0 we prove the first absolute upper bound on the am-plitude, independent of the physical constants, provided that Ɣ is sufficiently small. In any favorable case Ɣ ≤ 0 we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as Ɣ tends to-∞.

AB - sssWe consider classical steady water waves with a free surface, a flat bottom, and constant vorticity Ɣ. In the adverse case Ɣ > 0 we prove the first absolute upper bound on the am-plitude, independent of the physical constants, provided that Ɣ is sufficiently small. In any favorable case Ɣ ≤ 0 we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as Ɣ tends to-∞.

KW - amplitude

KW - free boundary

KW - vorticity

KW - water waves

UR - https://www.scopus.com/pages/publications/105038334770

UR - https://www.scopus.com/pages/publications/105038334770#tab=citedBy

U2 - 10.1137/24M1660565

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EP - 1830

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

AMPLITUDE BOUNDS OF STEADY ROTATIONAL WATER WAVES

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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