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Journal article
Well-posedness of two-dimensional hydroelastic waves
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, v 147(3), pp 529-570
Jun 2017
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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.
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Details
- Title
- Well-posedness of two-dimensional hydroelastic waves
- Creators
- David M Ambrose - Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA (ambrose@math.drexel.edu)Michael Siegel - Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA (misieg@njit.edu)
- Publication Details
- Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, v 147(3), pp 529-570
- Publisher
- Royal Society of Edinburgh Scotland Foundation; Edinburgh, UK
- Number of pages
- 42
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000402524500003
- Scopus ID
- 2-s2.0-85015628650
- Other Identifier
- 991014878292004721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied