Geodesic
Problems of stability and asymptotic behavior of vortex patches on the plane
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 2, pp. 327-343.

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With the help of mathematical modelling, we study the dynamics of many point vortices system on the plane. For this system, we consider the following cases: – vortex rings with outer radius $r=1$ and variable inner radius $r_0$, – vortex ellipses with semiaxes $a$, $b$. The emphasis is on the analysis of the asymptotic ($t\to\infty$) behavior of the system and on the verification of the stability criteria for vorticity continuous distributions.
Keywords: vortex dynamics, hydrodynamics, asymptotic behavior.
Mots-clés : point vortex 
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V. V. Vaskin; A. V. Vaskina; I. S. Mamaev. Problems of stability and asymptotic behavior of vortex patches on the plane. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 2, pp. 327-343. http://geodesic.mathdoc.fr/item/ND_2010_6_2_a6/

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