The 3D Nonlinear Schrodinger Equation with a Constant Magnetic Field Revisited

被引:2
|
作者
Dinh, Van Duong [1 ,2 ]
机构
[1] Ecole Normale Super Lyon, UMPA UMR 5669, CNRS, Lyon, France
[2] HCMC Univ Educ, Dept Math, 280 An Duong Vuong, Ho Chi Minh City, Vietnam
基金
欧洲研究理事会;
关键词
Nonlinear Schrodinger equation; Magnetic field; Global existence; Blow-up; Stability; STATIONARY STATES; NLS; OPERATORS; STABILITY;
D O I
10.1007/s10884-022-10235-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we revisit the Cauchy problem for the three dimensional nonlinear Schrodinger equation with a constant magnetic field. We first establish sufficient conditions that ensure the existence of global in time and finite time blow-up solutions. In particular, we derive sharp thresholds for global existence versus blow-up for the equation with mass-critical and mass-supercritical nonlinearities. We next prove the existence and orbital stability of normalized standing waves which extend the previous known results to the mass-critical and mass-supercritical cases. To show the existence of normalized solitary waves, we present a new approach that avoids the celebrated concentration-compactness principle. Finally, we study the existence and strong instability of ground state standing waves which greatly improve the previous literature.
引用
收藏
页数:44
相关论文
共 50 条