In the present note, we study the focusing NLS equation in dimension two with a point interaction in the supercritical regime, showing two results. After obtaining the (nonstandard) virial formula, we exhibit a set of initial data that shows blow-up. Moreover, we show that the standing waves eiωtφω corresponding to ground states φω of the action functional are strongly unstable, at least for sufficiently high ω .
Blow-up for the nonlinear Schrödinger equation with a point interaction in dimension two
Finco D;
2023-01-01
Abstract
In the present note, we study the focusing NLS equation in dimension two with a point interaction in the supercritical regime, showing two results. After obtaining the (nonstandard) virial formula, we exhibit a set of initial data that shows blow-up. Moreover, we show that the standing waves eiωtφω corresponding to ground states φω of the action functional are strongly unstable, at least for sufficiently high ω .File in questo prodotto:
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