Journal article
Well-posedness of 3D vortex sheets with surface tension
Communications in mathematical sciences, v 5(2), pp 391-430
01 Jan 2007
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Abstract
We prove well-posedness for the initial value problem for a vortex sheet in 3D fluids, in the presence of surface tension. We first reformulate the problem by making a favorable choice of variables and parameterizations. We then perform energy estimates for the evolution equations. It is important to note that the Kelvin-Helmholtz instability is present for the vortex sheet in the absence of surface tension. Accordingly, we must construct the energy functional carefully with an eye toward the regularization of this instability. Well-posedness follows from the estimates.
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Details
- Title
- Well-posedness of 3D vortex sheets with surface tension
- Creators
- David M. Ambrose - Clemson UniversityNader Masmoudi
- Publication Details
- Communications in mathematical sciences, v 5(2), pp 391-430
- Publisher
- INT PRESS
- Number of pages
- 40
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000247781200009
- Scopus ID
- 2-s2.0-34547194744
- Other Identifier
- 991019295180304721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied