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


[2] Constantin, P.; Titi, E. S., On the evolution of nearly circular vortex patches, Comm. Math. Phys., 119, 177-198 (1988) · Zbl 0673.76025
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