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Régularité du problème de Kelvin–Helmholtz pour l'équation d'Euler 2d

Published online by Cambridge University Press:  15 August 2002

Gilles Lebeau*
Affiliation:
Centre de Mathématiques, École Polytechnique, France ; lebeau@polytechnique.fr.
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Abstract

Nous prouvons que pour toute solution u du problème de Kelvin–Helmholtz des nappes de tourbillons pour l'équation d'Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de u et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de u sur t=0 lorsque u est définie sur un demi-interval [O,T[.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2002

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References

G. Birkhoff, Helmholtz et Taylor instability. Proc. Symp. Appl. Math XIII. Amer. Math. Soc. (1962) 55-76.
Bardos, C., Frisch, U., Sulem, C. et Sulem, P.L., Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability. CMP 80 (1981) 485-516.
Bony, J.-M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. Ec. Norm. Sup. IV 14 (1981) 209-246. CrossRef
Delort, J.-M., Existence de nappes de tourbillon en dimension deux. J. Amer. Math. Soc. 4 (1991) 553-586. CrossRef
Duchon, J. et Robert, R., Global vortex sheet solutions of Euler equation in the plane. J. Differential Equations 73 (1988) 215-224. CrossRef
G. Lebeau, Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d. Séminaire X-EDP 2000/2001, exposé 1 (2000).

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Régularité du problème de Kelvin–Helmholtz pour l'équation d'Euler 2d
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