Blowup Criterion for Viscous Baratropic Flows with Vacuum States

doi:10.1007/s00220-010-1148-y

	Blowup Criterion for Viscous Baratropic Flows with Vacuum States
	Huang, Xiangdi 1,4; Li, Jing 2,3,4; Xin, Zhouping 4
刊名	COMMUNICATIONS IN MATHEMATICAL PHYSICS
	2011
卷号	301 期号:1 页码:23-35
ISSN号	0010-3616
DOI	10.1007/s00220-010-1148-y
英文摘要	We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional (3D) barotropic compressible Navier-Stokes equations. More precisely, if a solution of the 3D barotropic compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (Ponce in Commun Math Phys 98:349-353, 1985). In addition, initial vacuum states are allowed in our cases.
资助项目	Zheng Ge Ru Foundation ; Hong Kong RGC[CUHK4028/04P] ; Hong Kong RGC[CUHK4040/06P] ; Hong Kong RGC[CUHK4042/08P] ; RGC[CA05/06.SC01] ; SRF for ROCS, SEM, NNSFC[1060105910971215]
WOS研究方向	Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000285787600002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/12523]
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Xiangdi
作者单位	1.Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China 2.Acad Sinica, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 3.Acad Sinica, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 4.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Huang, Xiangdi,Li, Jing,Xin, Zhouping. Blowup Criterion for Viscous Baratropic Flows with Vacuum States[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2011,301(1):23-35.
APA	Huang, Xiangdi,Li, Jing,&Xin, Zhouping.(2011).Blowup Criterion for Viscous Baratropic Flows with Vacuum States.COMMUNICATIONS IN MATHEMATICAL PHYSICS,301(1),23-35.
MLA	Huang, Xiangdi,et al."Blowup Criterion for Viscous Baratropic Flows with Vacuum States".COMMUNICATIONS IN MATHEMATICAL PHYSICS 301.1(2011):23-35.