On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum

doi:10.1002/mma.6255

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	On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum
	Lu, Boqiang 1; Wang, Yixuan 2; Wu, Yuhang 3
	2020-02-05
发表期刊	MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN	0170-4214
页码	24
摘要	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.
关键词	compressible Navier-Stokes equations density-dependent viscosity global classical solutions large-time behavior vacuum
DOI	10.1002/mma.6255
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11601218] ; National Natural Science Foundation of China[11971217]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000510979800001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50751
专题	中国科学院数学与系统科学研究院
通讯作者	Lu, Boqiang
作者单位	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
推荐引用方式 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.