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Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data
Guo, Zhenhua1,2; Wang, Mei1,2; Wang, Yi3,4
2018-04-01
Source PublicationNONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
ISSN1468-1218
Volume40Pages:260-289
AbstractIn this paper, we proved the global well-posedness of the solution to 3D spherically symmetric, compressible and isentropic Navier-Stokes equations in the whole space with arbitrarily large initial data when the shear viscosity mu is a positive constant and the bulk viscosity lambda(rho) = rho(beta) with 0 <= beta <= gamma and gamma > 1 being the adiabatic exponent in the gamma-law pressure. First, the global classical solution is obtained away from the symmetry center gamma = 0 with arbitrarily large and non-vacuum data. In particular, it is shown that the solution will not develop the vacuum states in any finite time away from the symmetry center if the initial density does not contain vacuum states. Then the global weak solutions with the symmetry center gamma = 0 are obtained as the limit of the classical solutions in the exterior domain of a ball B-epsilon(0) with the center at the origin and the radius epsilon > 0 when the ball shrink to the origin, that is, epsilon -> 0+, for any fixed total mass h > 0 defined in (3.1), and then let h -> 0+. (C) 2017 Elsevier Ltd. All rights reserved.
KeywordCompressible Navier-Stokes equations 3D spherically symmetric Global weak solution
DOI10.1016/j.nonrwa.2017.09.004
Language英语
Funding ProjectNational Natural Sciences Foundation of China[11331005] ; National Natural Sciences Foundation of China[11671385] ; SRDPC[20136101110015] ; Youth Innovation Promotion Association of CAS ; Young top-notch talent Program
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000416196800013
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29154
Collection应用数学研究所
Affiliation1.Northwest Univ, Sch Math, Xian 710069, Shaanxi, Peoples R China
2.Northwest Univ, CNS, Xian 710069, Shaanxi, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, CEMS,HCMS, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Guo, Zhenhua,Wang, Mei,Wang, Yi. Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2018,40:260-289.
APA Guo, Zhenhua,Wang, Mei,&Wang, Yi.(2018).Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data.NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,40,260-289.
MLA Guo, Zhenhua,et al."Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data".NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 40(2018):260-289.
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