Blow-up results for systems of nonlinear Schrodinger equations with quadratic interaction

被引：9

作者：

Dinh, Van Duong ^{[1
,2
]}

Forcella, Luigi ^{[3
,4
]}

机构：

[1] Univ Lille, Lab Paul Painleve, UMR 8524, CNRS, F-59655 Villeneuve Dascq, France

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

[3] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[4] Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2021年 / 72卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Nonlinear Schrodinger systems; Quadratic-type interactions; Blow-up; Grow-up; GROUND-STATE; SCATTERING; NLS; DYNAMICS;

D O I：

10.1007/s00033-021-01607-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.

引用

页数：26

共 29 条

[1] Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ3 nonlinear response [J].