A new highly nonlinear shallow water wave equation

Ronald Quirchmayr

doi:10.1007/s00028-015-0312-4

A new highly nonlinear shallow water wave equation

Ronald Quirchmayr

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.

Original language	English
Pages (from-to)	539-567
Number of pages	29
Journal	Journal of Evolution Equations
Volume	16
Issue number	3
Early online date	9 Jan 2016
DOIs	https://doi.org/10.1007/s00028-015-0312-4
Publication status	Published - Sept 2016

Austrian Fields of Science 2012

101002 Analysis

Keywords

Cubic nonlinearity
Large-amplitude waves
Shallow water equation
Well-posedness

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10.1007/s00028-015-0312-4

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title = "A new highly nonlinear shallow water wave equation",

abstract = "We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.",

keywords = "Cubic nonlinearity, Large-amplitude waves, Shallow water equation, Well-posedness",

author = "Ronald Quirchmayr",

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N2 - We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.

AB - We derive a quasilinear shallow water equation directly from the governing equations for gravity water waves within a certain regime for large-amplitude waves which has not been studied so far. Furthermore, we demonstrate local well-posedness of the corresponding Cauchy problem and finally discuss some aspects of the blowup behavior of solutions.

KW - Cubic nonlinearity

KW - Large-amplitude waves

KW - Shallow water equation

KW - Well-posedness

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DO - 10.1007/s00028-015-0312-4

M3 - Article

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SP - 539

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JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 3

ER -

A new highly nonlinear shallow water wave equation

Abstract

Austrian Fields of Science 2012

Keywords

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