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Dissertation
Well-posedness of hydroelastic waves and their truncated series models
Doctor of Philosophy (Ph.D.), Drexel University
Dec 2016
DOI:
https://doi.org/10.17918/etd-7743
Abstract
We study hydroelastic waves in two-dimensional irrotational, incompressible fluids. Each fluid 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 thesis is in two parts. The first part accounts for the mass of the elastic surface and evolves the tangent angle and arclength of the vortex sheet instead of Cartesian variables. Under the assumption that a certain integral equation is solvable, the initial value problem for the system is shown to be well-posed. It is demonstrated that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. In the second part, we study truncated series models of hydroelastic waves, ignoring the effects of mass. A strong dispersive term, which is relevant to the bending force of the elastic sheet, is added to a quadratic truncated series model of the water wave. Generalizing this somewhat, it is proved that when one adds a sufficiently strong dispersive term, including the case of hydroelastic dispersion, to the quadratic truncated series model, the system then has a well-posed initial value problem.
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Details
- Title
- Well-posedness of hydroelastic waves and their truncated series models
- Creators
- Shunlian Liu - DU
- Contributors
- David M. Ambrose (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- v, 112 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 7743; 991014632192004721