Communications in Mathematical Sciences

Well-posedness of 3D vortex sheets with surface tension

David M. Ambrose and Nader Masmoudi

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 9 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.cms/1183990372

Mathematical Reviews number (MathSciNet)
MR2334849

Zentralblatt MATH identifier
1130.76016

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

Keywords
vortex sheet surface tension Kelvin-Helmholtz instability well-posedness

Citation

Ambrose, David M.; Masmoudi, Nader. Well-posedness of 3D vortex sheets with surface tension. Commun. Math. Sci. 5 (2007), no. 2, 391--430. https://projecteuclid.org/euclid.cms/1183990372


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