Alinhac, Serge Remarques sur l’instabilité du problème des poches de tourbillon. (Remarks on the instability of the vortex patch problem). (French) Zbl 0732.35075 J. Funct. Anal. 98, No. 2, 361-379 (1991). 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)]. Reviewer: G.Pasa (Bucureşti) Cited in 4 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76U05 General theory of rotating fluids Keywords:vortex patch problem Citations:Zbl 0673.76025 × Cite Format Result Cite Review PDF 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.