Problems of stability and asymptotic behavior of vortex patches on the plane

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.