×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.