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Journal article
WELL-POSEDNESS OF A MODEL FOR WATER WAVES WITH VISCOSITY
Discrete and continuous dynamical systems. Series B, v 17(4), pp 1113-1137
01 Jun 2012
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Abstract
The water wave equations of ideal free-surface fluid mechanics are a fundamental model of open ocean movements with a surprisingly subtle well-posedness theory. In consequence of both theoretical and computational difficulties with the full water wave equations, various asymptotic approximations have been proposed, analyzed and used in practical situations. In this essay, we establish the well posedness of a model system of water wave equations which is inspired by recent work of Dias, Dyachenko, and Zakharov (Phys. Lett. A, 372:2008). The model in question includes dissipative effects and is weakly nonlinear. The present contribution is a first step in a larger program centered around the Dias-Dychenko-Zhakharov system.
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Details
- Title
- WELL-POSEDNESS OF A MODEL FOR WATER WAVES WITH VISCOSITY
- Creators
- David M. Ambrose - Drexel UniversityJerry L. Bona - Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USADavid P. Nicholls - Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USADepartment of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607
- Publication Details
- Discrete and continuous dynamical systems. Series B, v 17(4), pp 1113-1137
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- Number of pages
- 25
- Grant note
- DE-SC0001549 / Department of Energy; United States Department of Energy (DOE) University of Illinois at Chicago Universite de Paris Val de Marne agency of the United States Government 1016267 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS-0926378; DMS-1008387; DMS-1016267; DMS-0810958 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000301177800003
- Scopus ID
- 2-s2.0-84861694721
- Other Identifier
- 991019169411704721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied