On the blowing up of solutions to quantum hydrodynamic models on bounded domains

doi:10.1007/s00605-009-0092-4

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	On the blowing up of solutions to quantum hydrodynamic models on bounded domains
	Gamba, Irene M.1; Gualdani, Maria Pia 1; Zhang, Ping2
	2009-05-01
发表期刊	MONATSHEFTE FUR MATHEMATIK
ISSN	0026-9255
卷号	157 期号:1 页码:37-54
摘要	The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is based on a priori estimates for the energy functional for a new observable constructed with an auxiliary function, and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time.
关键词	Quantum hydrodynamic equations Blow-up of smooth solutions
DOI	10.1007/s00605-009-0092-4
语种	英语
资助项目	NSF[DMS0507038] ; Deutsche Forschungsgemeinschaft[JU359/5] ; Feodor Lynen Research fellowship ; NSF of China[10525101] ; NSF of China[10421101] ; Chinese Academy of Sciences ; Institute for Computational Engineering and Sciences at the University of Texas at Austin
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000265442400003
出版者	SPRINGER WIEN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8401
专题	数学所
通讯作者	Gamba, Irene M.
作者单位	1.Univ Texas Austin, Dept Math, Austin, TX 78712 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Gamba, Irene M.,Gualdani, Maria Pia,Zhang, Ping. On the blowing up of solutions to quantum hydrodynamic models on bounded domains[J]. MONATSHEFTE FUR MATHEMATIK,2009,157(1):37-54.
APA	Gamba, Irene M.,Gualdani, Maria Pia,&Zhang, Ping.(2009).On the blowing up of solutions to quantum hydrodynamic models on bounded domains.MONATSHEFTE FUR MATHEMATIK,157(1),37-54.
MLA	Gamba, Irene M.,et al."On the blowing up of solutions to quantum hydrodynamic models on bounded domains".MONATSHEFTE FUR MATHEMATIK 157.1(2009):37-54.