Communications in Mathematical Sciences

Well-posedness of 3D vortex sheets with surface tension

David M. Ambrose and Nader Masmoudi

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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.

Article information

Commun. Math. Sci., Volume 5, Issue 2 (2007), 391-430.

First available in Project Euclid: 9 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 76B07: Free-surface potential flows 35Q35: PDEs in connection with fluid mechanics

vortex sheet surface tension Kelvin-Helmholtz instability well-posedness


Ambrose, David M.; Masmoudi, Nader. Well-posedness of 3D vortex sheets with surface tension. Commun. Math. Sci. 5 (2007), no. 2, 391--430.

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