instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

	instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities
	Zaihui Gan; Boling Guo; Zhang Jian
	2009
发表期刊	Journal of Differential Equations
卷号	246 期号:10 页码:4097-4128
摘要	This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.
关键词	Klein–gordon–zakharov System Standing Wave Global Existence Blowup Instability
部门归属	计算机科学国家重点实验室
语种	英语
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/3140
专题	基础软件与系统重点实验室
推荐引用方式 GB/T 7714	Zaihui Gan,Boling Guo,Zhang Jian. instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities[J]. Journal of Differential Equations,2009,246(10):4097-4128.
APA	Zaihui Gan,Boling Guo,&Zhang Jian.(2009).instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities.Journal of Differential Equations,246(10),4097-4128.
MLA	Zaihui Gan,et al."instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities".Journal of Differential Equations 246.10(2009):4097-4128.

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