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Dissertation
A study of boundary-value problems in interfacial fluid dynamics
Doctor of Philosophy (Ph.D.), Drexel University
May 2011
DOI:
https://doi.org/10.17918/etd-3528
Abstract
We study two problems arising in interfacial fluid dynamics; a Boussinesq approximation equation derived by Bona, Chen and Saut for small amplitude long waterwaves, and a vortex sheet problem with fluids of the same densities. These problems are studied along with Dirichlet, Neumann, and mixed boundary conditions. We study a general elliptic partial differential equations for which we show the existence of non-periodic and periodic solutions. The proof of existence of these solutions uses techniques from the work of Duchon and Robert which relies on a fixed point type of estimate. The result is applied to the Boussinesq equations for periodic problems and the vortex sheet for non-periodic problems.
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Details
- Title
- A study of boundary-value problems in interfacial fluid dynamics
- Creators
- Timur Milgrom - 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
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 3528; 991014632666404721