BLOW-UP, GLOBAL EXISTENCE AND STANDING WAVES FOR THE MAGNETIC NONLINEAR SCHRODINGER EQUATIONS

Zaihui Gan; Jian Zhang

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BLOW-UP, GLOBAL EXISTENCE AND STANDING WAVES FOR THE MAGNETIC NONLINEAR SCHRODINGER EQUATIONS

机译：磁性非线性Schrodinger方程的爆破，整体存在性和平稳波动

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We study blow-up, global existence and standing waves for the nonlinear Schrodinger equations with two-dimensional magnetic field in a cold plasma. Under certain conditions on initial data and initial energy, we derive finite time blow-up phenomena of the solutions to the equations under study. Using compactness and Lagrange multiplier method, we establish the existence of standing waves. Finally, by introducing invariant manifolds and utilizing potential well argument as well as concavity method, we obtain the sharp threshold for global existence and blowup.

机译：我们研究冷等离子体中具有二维磁场的非线性Schrodinger方程的爆炸，整体存在和驻波。在初始数据和初始能量的特定条件下，我们得出了所研究方程组解的有限时间爆炸现象。使用紧致度和拉格朗日乘数法，我们建立了驻波的存在。最后，通过引入不变流形并利用势阱参数和凹度方法，我们获得了整体存在和爆炸的尖锐阈值。

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来源
《Discrete and continuous dynamical systems》 |2012年第3期|p.827-846|共20页
作者
Zaihui Gan; Jian Zhang;
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作者单位

College of Mathematics and Software Science Sichuan Normal University, Chengdu 610068, China;

College of Mathematics and Software Science Sichuan Normal University, Chengdu 610068, China;

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正文语种 eng
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关键词
nonlinear schrodinger equations; blow-up; global existence; magnetic field; standing wave;

机译：非线性薛定inger方程;爆炸;全球存在;磁场;驻波;

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1. Standing wave and global existence to nonlocal nonlinear Schrodinger equations: the two-dimensional case [J] . Gan Zaihui Nonlinearity . 2016,第7期

机译：非局部非线性薛定inger方程的驻波和整体存在：二维情况
2. Existence of stable standing waves for the fractional Schrodinger equations with combined power-type and Choquard-type nonlinearities [J] . Feng Binhua, Chen Ruipeng, Ren Jiajia Journal of Mathematical Physics . 2019,第5期

机译：具有型功率型和Chourding非线性的分数施罗德格方程稳定站立波的存在
3. Existence of stable standing waves for the fractional Schrodinger equations with combined nonlinearities [J] . Zhu Shihui Journal of evolution equations . 2017,第3期

机译：基于非线性的分数施罗德格方程存在稳定驻波
4. Global Existence and Blow-up of Weak Solutions for Nonlinear Wave Equations [C] . Yunzhu Gao, Wei Guo, Tian Luan International Conference on Advanced Design and Manufacturing Engineering . 2014

机译：非线性波动方程弱解的全局存在与爆破
5. Existence and multiplicity results on standing wave solutions of some coupled nonlinear Schrodinger equations. [D] . Tian, Rushun. 2013

机译：一类耦合非线性Schrodinger方程驻波解的存在性和多重性结果。
6. Blow-up of solutions of nonlinear wave equations in three space dimensions [O] . Fritz John 1979

机译：三维空间中非线性波动方程解的爆破
7. Existence and orbital stability of standing waves for some nonlinear Schrodinger equations, perturbation of a model case [O] . Genoud, Francois 2009

机译：非线性Schrodinger方程驻波的存在和轨道稳定性，模型的摄动。

BLOW-UP, GLOBAL EXISTENCE AND STANDING WAVES FOR THE MAGNETIC NONLINEAR SCHRODINGER EQUATIONS

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