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June 2007 Well-posedness of 3D vortex sheets with surface tension
David M. Ambrose, Nader Masmoudi
Commun. Math. Sci. 5(2): 391-430 (June 2007).


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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David M. Ambrose. Nader Masmoudi. "Well-posedness of 3D vortex sheets with surface tension." Commun. Math. Sci. 5 (2) 391 - 430, June 2007.


Published: June 2007
First available in Project Euclid: 9 July 2007

zbMATH: 1130.76016
MathSciNet: MR2334849

Primary: 35Q35 , 76B03 , 76B07

Keywords: Kelvin-Helmholtz instability , Surface tension , vortex sheet , well-posedness

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 2 • June 2007
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