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ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION
Cui, Jianbo1; Hong, Jialin; Sun, Liying
2019-12-01
Source PublicationDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN1531-3492
Volume24Issue:12Pages:6837-6854
AbstractIn this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schrodinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS equation in critical case. Meanwhile, the exponential integrability of the solution is proved, which implies the continuous dependence on the initial data. Then, we analyze the effect of the damped term and noise on the blow-up phenomenon. By modifying the associated energy, momentum and variance identity, we deduce a sharp blow-up condition for damped stochastic NLS equation in supercritical case. Moreover, we show that when the damped effect is large enough, the damped effect can prevent the blow-up of the solution with high probability.
KeywordStochastic nonlinear Schrodinger equation multiplicative noise global existence blow-up exponential integrability
DOI10.3934/dcdsb.2019169
Language英语
Funding ProjectNational Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000484545100025
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35690
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Cui, Jianbo,Hong, Jialin,Sun, Liying. ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2019,24(12):6837-6854.
APA Cui, Jianbo,Hong, Jialin,&Sun, Liying.(2019).ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,24(12),6837-6854.
MLA Cui, Jianbo,et al."ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 24.12(2019):6837-6854.
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