### 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) |
---|---|

Pages (from-to) | 391-430 |

Number of pages | 40 |

Journal | Communications in Mathematical Sciences |

Volume | 5 |

Issue number | 2 |

State | Published - 2007 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications in Mathematical Sciences*,

*5*(2), 391-430.

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

Research output: Contribution to journal › Article

*Communications in Mathematical Sciences*, vol. 5, no. 2, pp. 391-430.

}

TY - JOUR

T1 - Well-posedness of 3D vortex sheets with surface tension

AU - Ambrose, David M.

AU - Masmoudi, Nader

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Kelvin-Helmholtz instability

KW - Surface tension

KW - Vortex sheet

KW - Well-posedness

UR - http://www.scopus.com/inward/record.url?scp=34547194744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547194744&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34547194744

VL - 5

SP - 391

EP - 430

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

SN - 1539-6746

IS - 2

ER -