Journal article
The Zero Surface Tension Limit of Three-dimensional Water Waves
Indiana University mathematics journal, v 58(2), pp 479-521
01 Jan 2009
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Abstract
We establish that the limit of the water wave with surface tension, as surface tension vanishes, is the water wave without surface tension. The main tool is an energy estimate which is uniform in the surface tension parameter. Before establishing estimates, we reformulate the problem using suitable variables and an isothermal parameterization. With these variables and parameterizations, estimates for the water wave with or without surface tension are straightforward. In particular, this provides a new proof of existence of irrotational water waves in three space dimensions.
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Details
- Title
- The Zero Surface Tension Limit of Three-dimensional Water Waves
- Creators
- David M. Ambrose - Clemson UniversityNader Masmoudi - NYU, Courant Inst Math Sci, New York, NY 10012 USA
- Publication Details
- Indiana University mathematics journal, v 58(2), pp 479-521
- Publisher
- Indiana Univ Math Journal
- Number of pages
- 43
- Grant note
- DMS-0707807; DMS-0403983 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000265899500001
- Scopus ID
- 2-s2.0-67249144683
- Other Identifier
- 991019295192504721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics