Evolution of a cusp-like singularity in a vortex patch.

Raphaël Danchin

Revista Matemática Iberoamericana (2000)

  • Volume: 16, Issue: 2, page 281-329
  • ISSN: 0213-2230

Abstract

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We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a singular point, which generalizes the structure of the cusp. This entails the stability of cusp-like structures for all time with conservation of the order of the cusp.

How to cite

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Danchin, Raphaël. "Évolution d'une singularité de type cusp dans une poche de tourbillon.." Revista Matemática Iberoamericana 16.2 (2000): 281-329. <http://eudml.org/doc/39608>.

@article{Danchin2000,
author = {Danchin, Raphaël},
journal = {Revista Matemática Iberoamericana},
keywords = {Dinámica de fluidos; Hidrodinámica; Turbulencia; Tubo de torbellino; Puntos cuspidales; Singularidades},
language = {fre},
number = {2},
pages = {281-329},
title = {Évolution d'une singularité de type cusp dans une poche de tourbillon.},
url = {http://eudml.org/doc/39608},
volume = {16},
year = {2000},
}

TY - JOUR
AU - Danchin, Raphaël
TI - Évolution d'une singularité de type cusp dans une poche de tourbillon.
JO - Revista Matemática Iberoamericana
PY - 2000
VL - 16
IS - 2
SP - 281
EP - 329
LA - fre
KW - Dinámica de fluidos; Hidrodinámica; Turbulencia; Tubo de torbellino; Puntos cuspidales; Singularidades
UR - http://eudml.org/doc/39608
ER -

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