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On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum
Lu, Boqiang1; Wang, Yixuan2; Wu, Yuhang3
2020-02-05
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Pages24
AbstractFor the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global classical solution with large initial data containing vacuum. Furthermore, we show that the density is bounded from above independently of time, which yields the large time behavior of the solutions as time tends to infinity. More precisely, the density and the velocity converge to the steady states in Lp and in W1,p ( 1 <= p<+infinity), respectively. Moreover, the decay rate in time of the solutions is shown to be exponential. Finally, we also prove that the spatial gradient of density will blow up as time tends to infinity when the vacuum states appear initially even at one point.
Keywordcompressible Navier-Stokes equations density-dependent viscosity global classical solutions large-time behavior vacuum
DOI10.1002/mma.6255
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11601218] ; National Natural Science Foundation of China[11971217]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000510979800001
PublisherWILEY
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50751
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLu, Boqiang
Affiliation1.Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
3.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
Recommended Citation
GB/T 7714
Lu, Boqiang,Wang, Yixuan,Wu, Yuhang. On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2020:24.
APA Lu, Boqiang,Wang, Yixuan,&Wu, Yuhang.(2020).On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,24.
MLA Lu, Boqiang,et al."On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum".MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2020):24.
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