KMS Of Academy of mathematics and systems sciences, CAS
Blowup Criterion for Viscous Baratropic Flows with Vacuum States | |
Huang, Xiangdi1,4; Li, Jing2,3,4; Xin, Zhouping4 | |
2011 | |
Source Publication | COMMUNICATIONS IN MATHEMATICAL PHYSICS
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ISSN | 0010-3616 |
Volume | 301Issue:1Pages: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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