On the well-posedness for Keller-Segel system with fractional diffusion

doi:10.1002/mma.1480

CSpace

	On the well-posedness for Keller-Segel system with fractional diffusion
	Wu, Gang 1; Zheng, Xiaoxin 2
	2011-09-30
发表期刊	MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN	0170-4214
卷号	34 期号:14 页码:1739-1750
摘要	In this paper, we study the Cauchy problem for the Keller-Segel system with fractional diffusion generalizing the Keller-Segel model of chemotaxis for the initial data (u(0), v(0)) in critical Fourier-Herz spaces <(B)over dot>(2-2 alpha)(q) (R(n)) x <(B)over dot>(2-alpha)(q) (R(n)) with q is an element of [2, infinity], where 1< alpha <= 2. Making use of some estimates of the linear dissipative equation in the frame of mixed time-space spaces, the Chemin 'mono-norm method', the Fourier localization technique and the Littlewood-Paley theory, we get a local well-posedness result and a global well-posedness result with a small initial data. In addition, ill-posedness for 'doubly parabolic' models is also studied. Copyright (C) 2011 John Wiley & Sons, Ltd.
关键词	nonlinear parabolic equations nonlinear evolution equations fractional diffusion Keller-Segel model Well-posedness Ill-posedness
DOI	10.1002/mma.1480
语种	英语
资助项目	Chinese Postdoctoral Science Foundation[20090460553]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000294324900007
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11788
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Gang
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China
推荐引用方式 GB/T 7714	Wu, Gang,Zheng, Xiaoxin. On the well-posedness for Keller-Segel system with fractional diffusion[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2011,34(14):1739-1750.
APA	Wu, Gang,&Zheng, Xiaoxin.(2011).On the well-posedness for Keller-Segel system with fractional diffusion.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,34(14),1739-1750.
MLA	Wu, Gang,et al."On the well-posedness for Keller-Segel system with fractional diffusion".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 34.14(2011):1739-1750.