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Well-posedness of two-dimensional hydroelastic waves with mass
Journal article   Open access   Peer reviewed

Well-posedness of two-dimensional hydroelastic waves with mass

Shunlian Liu and David M. Ambrose
Journal of Differential Equations, v 262(9), pp 4656-4699
05 May 2017
DOI: https://doi.org/10.1016/j.jde.2016.12.016
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url
https://doi.org/10.1016/j.jde.2016.12.016View
Published, Version of Record (VoR)Open Access (Publisher-Specific),  Open

Abstract

Mathematics Physical Sciences Science & Technology
We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved well-posedness without considering the mass of the elastic surface; we now consider the effect of this mass. Under the assumption that a certain integral equation is solvable, we prove well-posedness of the initial value problem for the system. We are able to demonstrate that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. The proof uses geometric dependent variables, a normalized arclength parameterization, and a small-scale decomposition in the evolution equations. (C) 2016 Elsevier Inc. All rights reserved.

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