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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)].

35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
Zbl 0673.76025
Full Text: DOI
[1] {\scJ. Y. Chemin}, Article à paraître.
[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)
[4] Yudovitch, V.I, Flots non stationnaires d’un fluide ideal incompressible, Zh. vychisl. mat. i mat. fiz., 3, 1032-1066, (1963), [en russe]
[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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