## 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.

Original language | English (US) |
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Pages (from-to) | 529-570 |

Number of pages | 42 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 147 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2017 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- energy method
- hydroelastic waves
- vortex sheet
- well-posedness