Global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains

被引：0

作者：

Kexin Li ^{[1
]}

Boqiang Lü ^{[2
]}

Yixuan Wang ^{[3
]}

机构：

[1] School of Mathematical Sciences, Beijing Normal University

[2] College of Mathematics and Information Science, Nanchang Hangkong University

[3] Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

来源：

ScienceChina(Mathematics) | 2021年 / 64卷 / 06期

基金：

中国国家自然科学基金;

关键词：

1D compressible Navier-Stokes equations; global well-posedness; large initial data; vacuum; density-depending viscosity;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for one-dimensional(1D) barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces. Under a general assumption on the densitydepending viscosity, we prove that the Cauchy problem admits a unique global strong(classical) solution for the large initial data with vacuum. Moreover, the density is proved to be bounded from above time-independently.As a consequence, we obtain the large time behavior of the solution without external forces.

引用

页码：1231 / 1244

页数：14

共 16 条

[1] On global classical solutions to 1D compressible Navier-Stokes equations with density-dependent viscosity and vacuum
Lu, Boqiang
Wang, Yixuan
Wu, Yuhang
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5127 - 5150
[2] Global classical solution to 1D compressible Navier–Stokes equations with no vacuum at infinity[J] . Yulin Ye.Math. Meth. Appl. Sci. . 2016 (4)
[3] ON THE GLOBAL MOTION OF VISCOUS COMPRESSIBLE BAROTROPIC FLOWS SUBJECT TO LARGE EXTERNAL POTENTIAL FORCES AND VACUUM
Li, Jing
Zhang, Jianwen
Zhao, Junning
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (02) : 1121 - 1153
[4] Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows[J] . Xiangdi Huang,Jing Li.Communications in Mathematical Physics . 2013 (1)
[5] On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier–Stokes equations with vacuum[J] . Jing Li,Zhilei Liang.Journal de mathématiques pures et appliquées . 2013
[6] Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations
Huang, Xiangdi
Li, Jing
Xin, Zhouping
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (04) : 549 - 585
[7] Global classical large solutions to 1D compressible Navier–Stokes equations with density-dependent viscosity and vacuum[J] . Shijin Ding,Huanyao Wen,Changjiang Zhu.Journal of Differential Equations . 2011 (6)
[8] Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data ☆ ☆ Partially supported by the National Natural Scienc[J] . Feimin Huang,Jing Li,Zhouping Xin.Journal de mathématiques pures et appliquées . 2006 (6)
[9] On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
Cho, YG
Kim, H
[J]. MANUSCRIPTA MATHEMATICA, 2006, 120 (01) : 91 - 129
[10] Some uniform estimates and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows[J] . Jing Li,Zhouping Xin.Journal of Differential Equations . 2005 (2)

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