FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

doi:10.1016/S0252-9602(15)30082-5

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 111-123.doi: 10.1016/S0252-9602(15)30082-5

FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

连汝续^1,2, 刘健³

1. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
3. College of Teacher Education, Quzhou University, Quzhou 324000, China

收稿日期:2014-10-26 修回日期:2014-12-12 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Ruxu LIAN,E-mail:ruxu.lian.math@gmail.com;Jian LIU,E-mail:liujian.maths@gmail.com
基金资助:
The research of R.X. Lian is supported by NNSFC(11101145), China Postdoctoral Science Foundation(2012M520360), Doctoral Foundation of North China University of Water Sources and Electric Power(201032), Innovation Scientists and Technicians Troop Construction Projects of Henan Province. The research of J. Liu is supported by NNSFC(11326140 and 11501323), the Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313).

FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

Ruxu LIAN^1,2, Jian LIU³

1. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
3. College of Teacher Education, Quzhou University, Quzhou 324000, China

Received:2014-10-26 Revised:2014-12-12 Online:2016-01-30 Published:2016-01-30
Supported by:
The research of R.X. Lian is supported by NNSFC(11101145), China Postdoctoral Science Foundation(2012M520360), Doctoral Foundation of North China University of Water Sources and Electric Power(201032), Innovation Scientists and Technicians Troop Construction Projects of Henan Province. The research of J. Liu is supported by NNSFC(11326140 and 11501323), the Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313).

摘要/Abstract

摘要：

In this paper, we investigate the free boundary value problem(FBVP) for the cylindrically symmetric isentropic compressible Navier-Stokes equations(CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

关键词: cylindrically symmetric Navier-Stokes equations, free boundary value problem, density-dependent viscosity coefficients, strong solution

Abstract:

Key words: cylindrically symmetric Navier-Stokes equations, free boundary value problem, density-dependent viscosity coefficients, strong solution

中图分类号:

35Q35

连汝续, 刘健. FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(1): 111-123.

Ruxu LIAN, Jian LIU. FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. Acta mathematica scientia,Series B, 2016, 36(1): 111-123.

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FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

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