Blowup Criterion for Viscous Baratropic Flows with Vacuum States

doi:10.1007/s00220-010-1148-y

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	Blowup Criterion for Viscous Baratropic Flows with Vacuum States
	Huang, Xiangdi 1,4; Li, Jing 2,3,4; Xin, Zhouping 4
	2011
Source Publication	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
Volume	301 Issue:1 Pages:23-35
Abstract	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.
DOI	10.1007/s00220-010-1148-y
Language	英语
Funding Project	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 Research Area	Physics
WOS Subject	Physics, Mathematical
WOS ID	WOS:000285787600002
Publisher	SPRINGER
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/12524
Collection	中国科学院数学与系统科学研究院
Corresponding Author	Huang, Xiangdi
Affiliation	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
Recommended Citation 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.

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