SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION

doi:10.1137/20M1369749

	SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION
	Gui, Guilong 3; Zhang, Ping 1,2,4
刊名	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
	2022
卷号	54 期号:1 页码:1053-1104
关键词	semiclassical limit Schrodinger equation boundary layer successive complementary expansion method
ISSN号	0036-1410
DOI	10.1137/20M1369749
英文摘要	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.
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
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000762768000031
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60139]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China 4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, 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.