# Numerical evidence of nonuniqueness in the evolution of vortex sheets

Milton C. Lopes Filho; John Lowengrub; Helena J. Nussenzveig Lopes; Yuxi Zheng

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 2, page 225-237
- ISSN: 0764-583X

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topLopes Filho, Milton C., et al. "Numerical evidence of nonuniqueness in the evolution of vortex sheets." ESAIM: Mathematical Modelling and Numerical Analysis 40.2 (2006): 225-237. <http://eudml.org/doc/249718>.

@article{LopesFilho2006,

abstract = {
We consider a special configuration of vorticity that consists of a pair of
externally tangent circular vortex sheets, each having a circularly symmetric core
of bounded vorticity concentric to the sheet, and each core precisely balancing the
vorticity mass of the sheet. This configuration is a stationary weak solution of the
2D incompressible Euler equations. We propose to perform numerical experiments to verify
that certain approximations of this flow configuration converge to a non-stationary
weak solution. Preliminary simulations presented here suggest this is
indeed the case. We establish a convergence theorem for the vortex blob method that
applies to this problem. This theorem and the preliminary calculations we carried out
support the existence of two distinct weak solutions with the same initial data.
},

author = {Lopes Filho, Milton C., Lowengrub, John, Nussenzveig Lopes, Helena J., Zheng, Yuxi},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonuniqueness; vortex sheets; vortex methods; Euler equations.; weak solution; incompressible Euler equations; convergence; vortex blob method},

language = {eng},

month = {6},

number = {2},

pages = {225-237},

publisher = {EDP Sciences},

title = {Numerical evidence of nonuniqueness in the evolution of vortex sheets},

url = {http://eudml.org/doc/249718},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Lopes Filho, Milton C.

AU - Lowengrub, John

AU - Nussenzveig Lopes, Helena J.

AU - Zheng, Yuxi

TI - Numerical evidence of nonuniqueness in the evolution of vortex sheets

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/6//

PB - EDP Sciences

VL - 40

IS - 2

SP - 225

EP - 237

AB -
We consider a special configuration of vorticity that consists of a pair of
externally tangent circular vortex sheets, each having a circularly symmetric core
of bounded vorticity concentric to the sheet, and each core precisely balancing the
vorticity mass of the sheet. This configuration is a stationary weak solution of the
2D incompressible Euler equations. We propose to perform numerical experiments to verify
that certain approximations of this flow configuration converge to a non-stationary
weak solution. Preliminary simulations presented here suggest this is
indeed the case. We establish a convergence theorem for the vortex blob method that
applies to this problem. This theorem and the preliminary calculations we carried out
support the existence of two distinct weak solutions with the same initial data.

LA - eng

KW - Nonuniqueness; vortex sheets; vortex methods; Euler equations.; weak solution; incompressible Euler equations; convergence; vortex blob method

UR - http://eudml.org/doc/249718

ER -

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