  In the present note we study the NLS equation in dimension two with a point
interaction and in the supercritical regime, showing two results. After
obtaining the (nonstandard) virial formula, we exhibit a set of initial data
that blow-up. Moreover we show the standing waves $e^{i\omega t}
\varphi_\omega$ corresponding to ground states $\varphi_\omega$ of the action
are strongly unstable, at least for sufficiently high $\omega$.
