Well-posedness of two-dimensional hydroelastic waves

Document Type

Conference Proceeding

Publication Date

6-1-2017

Abstract

A well-posedness theory for the initial-value problem for hydroelastic waves in two spatial dimensions is presented. This problem, which arises in numerous applications, describes the evolution of a thin elastic membrane in a two-dimensional (2D) potential flow. We use a model for the elastic sheet that accounts for bending stresses and membrane tension, but which neglects the mass of the membrane. The analysis is based on a vortex sheet formulation and, following earlier analyses and numerical computations in 2D interfacial flow with surface tension, we use an angle-arclength representation of the problem. We prove short-time well-posedness in Sobolev spaces. The proof is based on energy estimates, and the main challenge is to find a definition of the energy and estimates on high-order non-local terms so that an a priori bound can be obtained.

Identifier

85015628650 (Scopus)

Publication Title

Proceedings of the Royal Society of Edinburgh Section A Mathematics

External Full Text Location

https://doi.org/10.1017/S0308210516000238

e-ISSN

14737124

ISSN

03082105

First Page

529

Last Page

570

Issue

3

Volume

147

Grant

DMS-1009105

Fund Ref

National Science Foundation

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