# Well-posedness of 3D vortex sheets with surface tension

Research output: Contribution to journalArticle

### 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.

Original language English (US) 391-430 40 Communications in Mathematical Sciences 5 2 Published - 2007

### Fingerprint

Vortex Sheet
Surface Tension
Well-posedness
Surface tension
Vortex flow
Kelvin-Helmholtz Instability
Initial value problems
Energy Estimates
Energy Functional
Parameterization
Evolution Equation
Initial Value Problem
Regularization
Fluid
Fluids
Estimate

### Keywords

• Kelvin-Helmholtz instability
• Surface tension
• Vortex sheet
• Well-posedness

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

Well-posedness of 3D vortex sheets with surface tension. / Ambrose, David M.; Masmoudi, Nader.

In: Communications in Mathematical Sciences, Vol. 5, No. 2, 2007, p. 391-430.

Research output: Contribution to journalArticle

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