On instability of standing waves for the mass-supercritical fractional nonlinear Schrodinger equation

被引：14

作者：

Van Duong Dinh ^{[1
,2
]}

机构：

[1] Univ Toulouse, CNRS, UMR5219, Inst Math Toulouse, F-31062 Toulouse 9, France

[2] HCMC Univ Pedag, Dept Math, 280 An Duong Vuong, Ho Chi Minh, Vietnam

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2019年 / 70卷 / 02期

关键词：

Fractional nonlinear Schrodinger equation; Standing wave; Instability; Localized virial estimate; Blow-up; STABILITY; EXISTENCE; BLOWUP;

D O I：

10.1007/s00033-019-1104-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the focusing L-2-supercritical fractional nonlinear Schrodinger equation By means of the localized virial estimate, we prove that the ground-state standing wave is strongly unstable by blowup. This result is a complement to a recent result of Peng-Shi (J Math Phys 59: 011508, 2018) where the stability and instability of standing waves were studied in the L-2-subcritical and L-2-critical cases.

引用

页数：17

共 50 条

[1] On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation
Van Duong Dinh
[J]. Zeitschrift für angewandte Mathematik und Physik, 2019, 70
[2] Concentrating standing waves for the fractional nonlinear Schrodinger equation
Davila, Juan
del Pino, Manuel
Wei, Juncheng
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (02) : 858 - 892
[3] Stability of Standing Waves for the Nonlinear Fractional Schrodinger Equation
Zhang, Jian
Zhu, Shihui
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2017, 29 (03) : 1017 - 1030
[4] On stability and instability of standing waves for the inhomogeneous fractional Schrodinger equation
Liu, Jiayin
[J]. AIMS MATHEMATICS, 2020, 5 (06): : 6298 - 6312
[5] Stability and instability of standing waves for the fractional nonlinear Schrodinger equations
Feng, Binhua
Zhu, Shihui
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 292 : 287 - 324
[6] Instability of standing waves for nonlinear Schrodinger equation with delta potential
Ohta, Masahito
[J]. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019, 13 (02): : 465 - 474
[7] Instability of Standing Waves for the Nonlinear Schrodinger Equation with Energy Critical Growth
Zhang, Yue
Zhang, Jian
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022,
[8] Stability and instability of standing waves for the nonlinear Schrodinger equation with harmonic potential
Fukuizumi, R
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2001, 7 (03) : 525 - 544
[9] INSTABILITY OF STANDING WAVES TO THE INHOMOGENEOUS NONLINEAR SCHRODINGER EQUATION WITH HARMONIC POTENTIAL
Chen, Jianqing
Liu, Yue
[J]. ILLINOIS JOURNAL OF MATHEMATICS, 2008, 52 (04) : 1259 - 1276
[10] On global existence for mass-supercritical nonlinear fractional Hartree equations
Wu, Dan
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2017, 33 (02): : 389 - 400

← 1 2 3 4 5 →