SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION

doi:10.1137/20M1369749

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	SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION
	Gui, Guilong 1; Zhang, Ping 2,3,4
	2022
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	54 期号:1 页码:1053-1104
摘要	In this paper, we justify the semiclassical limit of the Gross-Pitaevskii equation with Dirichlet boundary condition on the three-dimensional upper space under the assumption that the leading-order terms to both initial amplitude and initial phase function are sufficiently small in some high enough Sobolev norms. We remark that the main difficulty of the proof lies in the fact that the boundary layer appears in the leading-order terms of the amplitude functions and the gradient of the phase functions to the WKB expansions of the solutions. In particular, we partially solved the open question proposed in [D. Chiron and F. Rousset, Comm. Math. Phys., 288 (2009), pp. 503-546; C. T. Pham, C. Nore, and M. E. Brachet, Phys. D, 210 (2005), pp. 203-226] concerning the semiclassical limit of the Gross-Pitaevskii equation with Dirichlet boundary condition.
关键词	semiclassical limit Schrodinger equation boundary layer successive complementary expansion method
DOI	10.1137/20M1369749
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China (NSFC)[11571279] ; K. C. Wong Education Foundation ; NSFC[11731007] ; NSFC[12031006] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000762768000031
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60140
专题	中国科学院数学与系统科学研究院
通讯作者	Gui, Guilong
作者单位	1.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Gui, Guilong,Zhang, Ping. SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2022,54(1):1053-1104.
APA	Gui, Guilong,&Zhang, Ping.(2022).SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,54(1),1053-1104.
MLA	Gui, Guilong,et al."SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 54.1(2022):1053-1104.