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Blowup Criterion for Viscous Baratropic Flows with Vacuum States
Huang, Xiangdi1,4; Li, Jing2,3,4; Xin, Zhouping4
2011
Source PublicationCOMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN0010-3616
Volume301Issue:1Pages:23-35
AbstractWe 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.
DOI10.1007/s00220-010-1148-y
Language英语
Funding ProjectZheng 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 AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000285787600002
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12524
Collection中国科学院数学与系统科学研究院
Corresponding AuthorHuang, Xiangdi
Affiliation1.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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