KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | MATHEMATICAL METHODS IN THE APPLIED SCIENCES |
ISSN | 0170-4214 |
Pages | 24 |
Abstract | For 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. |
Keyword | compressible Navier-Stokes equations density-dependent viscosity global classical solutions large-time behavior vacuum |
DOI | 10.1002/mma.6255 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11601218] ; National Natural Science Foundation of China[11971217] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000510979800001 |
Publisher | WILEY |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50751 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Lu, Boqiang |
Affiliation | 1.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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