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SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION
Gui, Guilong1; Zhang, Ping2,3,4
2022
Source PublicationSIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN0036-1410
Volume54Issue:1Pages:1053-1104
AbstractIn 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.
Keywordsemiclassical limit Schrodinger equation boundary layer successive complementary expansion method
DOI10.1137/20M1369749
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China (NSFC)[11571279] ; K. C. Wong Education Foundation ; NSFC[11731007] ; NSFC[12031006] ; NSFC[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000762768000031
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60140
Collection中国科学院数学与系统科学研究院
Corresponding AuthorGui, Guilong
Affiliation1.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
Recommended Citation
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.
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