Sharp scattering for the cubic-quintic nonlinear Schrodinger equation in the focusing-focusing regime

被引：8

作者：

Luo, Yongming ^{[1
]}

机构：

[1] Tech Univ Dresden, Inst Wissensch Rechnen, Zellescher Weg 12-14, D-01069 Dresden, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 283卷 / 01期

关键词：

Cubic-quintic Schrodinger equation; Scattering threshold; Combined nonlinearities; GLOBAL WELL-POSEDNESS; SCALAR FIELD-EQUATIONS; POSITIVE SOLUTIONS; STANDING WAVES; GROUND-STATE; BLOW-UP; EXISTENCE; MASS; NLS;

D O I：

10.1016/j.jfa.2022.109489

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the large data scattering problem for the 2D and 3D cubic-quintic nonlinear Schrodinger equation in the focusing-focusing regime. Our attention is firstly restricted to the 2D space, where the cubic nonlinearity is L2-critical. We establish a new type of scattering criterion that is uniquely determined by the mass of the initial data, which differs from the classical setting based on the Lyapunov functional. At the end, we formulate a solely mass-determining scattering threshold for the 3D cubic-quintic nonlinear Schrodinger equation in the focusing-focusing regime. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：34

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