ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION

doi:10.3934/dcdsb.2019169

	ON GLOBAL EXISTENCE AND BLOW-UP FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION
	Cui, Jianbo 1; Hong, Jialin; Sun, Liying
	2019-12-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN	1531-3492
卷号	24 期号:12 页码:6837-6854
摘要	In 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.
关键词	Stochastic nonlinear Schrodinger equation multiplicative noise global existence blow-up exponential integrability
DOI	10.3934/dcdsb.2019169
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000484545100025
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35690
专题	计算数学与科学工程计算研究所
通讯作者	Cui, Jianbo
作者单位	1.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
推荐引用方式 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.