BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS

doi:10.3934/dcds.2017159

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 数学物理与应用研究部

	BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS
	Zhou, Huan-Song 2; Guo, Yujin 1; Zeng, Xiaoyu 2
刊名	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
	2017-07-01
卷号	37 期号:7 页码:3749-3786
关键词	Schrodinger Equations Gross-pitaevskii Equation Elliptic Systems Constrained Minimization Blow Up
DOI	10.3934/dcds.2017159
文献子类	Article
英文摘要	The paper is concerned with a system of two coupled time-independent Gross-Pitaevskii equations in R-2, which is used to model two-component Bose-Einstein condensates with both attractive intraspecies and attractive interspecies interactions. This system is essentially an eigenvalue problem of a stationary nonlinear Schriidinger system in R-2, and solutions of the problem are obtained by seeking minimizers of the associated variational functional with constrained mass (i.e. L-2 norm constaints). Under a certain type of trapping potentials V-i(x) (i = 1, 2), the existence, non-existence and uniqueness of this kind of solutions are studied. Moreover, by establishing some delicate energy estimates, we show that each component of the solutions blows up at the same point (i.e., one of the global minima of V-i(x)) when the total interaction strength of intraspecies and interspecies goes to a critical value. An optimal blowing up rate for the solutions of the system is also given.
WOS关键词	NONLINEAR SCHRODINGER SYSTEM ; CONCENTRATION-COMPACTNESS PRINCIPLE ; SYMMETRY-BREAKING ; GROUND-STATES ; PHASE-SEPARATION ; SOLITARY WAVES ; BOUND-STATES ; BIFURCATION ; POTENTIALS ; EXISTENCE
WOS研究方向	Mathematics
语种	英语
WOS记录号	WOS:000401072700010
资助机构	NSFC(11322104 ; NSFC(11322104 ; 11671394 ; 11671394 ; 11501555 ; 11501555 ; 11471331) ; 11471331) ; NSFC(11322104 ; NSFC(11322104 ; 11671394 ; 11671394 ; 11501555 ; 11501555 ; 11471331) ; 11471331)
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/11308]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Peoples R China 2.Wuhan Univ Technol, Sch Sci, Dept Math, Wuhan 430070, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Huan-Song,Guo, Yujin,Zeng, Xiaoyu. BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2017,37(7):3749-3786.
APA	Zhou, Huan-Song,Guo, Yujin,&Zeng, Xiaoyu.(2017).BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,37(7),3749-3786.
MLA	Zhou, Huan-Song,et al."BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 37.7(2017):3749-3786.