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 ?.

引用

页数：17

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