Blow-up and instability of standing waves for the NLS with a point interaction in dimension two

被引：3
|
作者：
Finco, Domenico [1 ]
Noja, Diego [2 ]
机构：
[1] Univ Telemat Int Uninettuno, Fac Ingn, Corso Vittorio Emanuele 2 39, I-00186 Rome, Italy
[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Roberto Cozzi 55, I-20126 Milan, Italy
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2023年 / 74卷 / 04期
关键词：
Nonlinear Schrodinger equation; Point interactions; Blow-up; Instability of standing waves; NONLINEAR SCHRODINGER-EQUATION; STABILITY; STATES;
D O I：
10.1007/s00033-023-02056-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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?t)?? corresponding to ground states ?? of the action functional are strongly unstable, at least for sufficiently high ?.
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页数：17
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