KMS Of Academy of mathematics and systems sciences, CAS
SEMICLASSICAL LIMIT OF GROSS-PITAEVSKII EQUATION WITH DIRICHLET BOUNDARY CONDITION | |
Gui, Guilong1; Zhang, Ping2,3,4 | |
2022 | |
Source Publication | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
ISSN | 0036-1410 |
Volume | 54Issue:1Pages:1053-1104 |
Abstract | 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. |
Keyword | semiclassical limit Schrodinger equation boundary layer successive complementary expansion method |
DOI | 10.1137/20M1369749 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China (NSFC)[11571279] ; K. C. Wong Education Foundation ; NSFC[11731007] ; NSFC[12031006] ; NSFC[11688101] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000762768000031 |
Publisher | SIAM PUBLICATIONS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60140 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Gui, Guilong |
Affiliation | 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 |
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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