论文标题
NLS的站立波的爆炸和不稳定性在尺寸二的点相互作用
Blow-up and instability of standing waves for the NLS with a point interaction in dimension two
论文作者
论文摘要
在本说明中，我们研究了二维和超临界状态的NLS方程，显示了两个结果。获得（非标准）病毒公式后，我们展示了一组爆炸的初始数据。此外，我们显示了与基础状态相对应的操作的$ e^{iΩt}φ的$ e^{iΩt}φ_Ω$，至少对于足够高的$ω$而言，这是非常不稳定的。
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 $e^{iωt} φ_ω$ corresponding to ground states $φ_ω$ of the action are strongly unstable, at least for sufficiently high $ω$.
