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Remarques sur l’instabilité du problème des poches de tourbillon. (Remarks on the instability of the vortex patch problem). (French) Zbl 0732.35075

The author considers the two-dimensional Euler equation with an initial vortex being the characteristic function of some domain, given by a boundary T. The main result is an instability in finite time of this boundary T (which is considered closed to a unit circle). Perturbation equations are of second order. The method is related with the paper of P. Constantin and E. S. Titi [Commun. Math. Phys. 119, No.2, 177-198 (1988; Zbl 0673.76025)].

MSC:

35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids

Citations:

Zbl 0673.76025
Full Text: DOI

References:

[2] Constantin, P.; Titi, E. S., On the evolution of nearly circular vortex patches, Comm. Math. Phys., 119, 177-198 (1988) · Zbl 0673.76025
[3] Majda, A., Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math., 39, 187-220 (1986) · Zbl 0595.76021
[4] Yudovitch, V. I., Flots non stationnaires d’un fluide ideal incompressible, Zh. Vychisl. Mat. i Mat. Fiz., 3, 1032-1066 (1963), [en russe] · Zbl 0129.19402
[5] Zabusky, N.; Hughes, M. H.; Roberts, K. V., Contour dynamics for the Euler equations in two dimensions, J. Comp. Phys., 30, 96-106 (1979) · Zbl 0405.76014
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