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SUFFICIENTLY STRONG DISPERSION REMOVES ILL-POSEDNESS IN TRUNCATED SERIES MODELS OF WATER WAVES
Journal article   Open access   Peer reviewed

SUFFICIENTLY STRONG DISPERSION REMOVES ILL-POSEDNESS IN TRUNCATED SERIES MODELS OF WATER WAVES

Shunlian Liu, David M. Ambrose and School of Science, Hunan University of Technology, Zhuzhou, Hunan 412007, China
Discrete and continuous dynamical systems. Series A, v 39(6), pp 3123-3147
01 Jun 2019
DOI: https://doi.org/10.3934/dcds.2019129
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url
https://doi.org/10.3934/dcds.2019129View
Published, Version of Record (VoR)CC BY V4.0,  Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Truncated series models of gravity water waves are popular for use in simulation. Recent work has shown that these models need not inherit the well-posedness properties of the full equations of motion (the irrotational, incompressible Euler equations). We show that if one adds a sufficiently strong dispersive term to a quadratic truncated series model, the system then has a well-posed initial value problem. Such dispersion can be relevant in certain physical contexts, such as in the case of a bending force present at the free surface, as in a hydroelastic sheet.

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3 citations in Scopus

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#14 Life Below Water

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Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Mathematics
Mathematics, Applied
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