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Blow-up and instability of standing waves for the NLS with a point interaction in dimension two
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Blow-up and instability of standing waves for the NLS with a point interaction in dimension two
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Journal Article
Blow-up and instability of standing waves for the NLS with a point interaction in dimension two
2023
Overview
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
e
i
ω
t
φ
ω
corresponding to ground states
φ
ω
of the action functional are strongly unstable, at least for sufficiently high
ω
.
Publisher
Springer International Publishing,Springer Nature B.V
