CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

doi:10.1016/S0252-9602(12)60019-8

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (1): 315-324.doi: 10.1016/S0252-9602(12)60019-8

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

连汝续¹, 刘健², 李海梁², 肖玲³

1. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Department of Mathematics, Capital Normal University, Beijing 100048, China;
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2011-11-17 出版日期:2012-01-20 发布日期:2012-01-20
基金资助:
The research of R.X. Lian is supported by NSFC (11101145). The research of H.L. Li is partially supported by NSFC (10871134, 11171228), the Huo Ying Dong Fund (111033), the Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201006107). The research of L. Xiao is supported by NSFC (11171327).

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

LIAN Ru-Xu¹, LIU Jian², LI Hai-Liang², XIAO Ling³

1. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Department of Mathematics, Capital Normal University, Beijing 100048, China;
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2011-11-17 Online:2012-01-20 Published:2012-01-20
Supported by:
The research of R.X. Lian is supported by NSFC (11101145). The research of H.L. Li is partially supported by NSFC (10871134, 11171228), the Huo Ying Dong Fund (111033), the Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201006107). The research of L. Xiao is supported by NSFC (11171327).

摘要/Abstract

摘要：

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coe?cient. For regular initial data, we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically. When initial density is piecewise regular with jump discontinuity, we show that there exists a unique global piecewise regular solution. In
particular, the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t → +∞.

关键词: Navier-Stokes equations, discontinuous initial data

Abstract:

Key words: Navier-Stokes equations, discontinuous initial data

中图分类号:

35B40

连汝续, 刘健, 李海梁, 肖玲. CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(1): 315-324.

LIAN Ru-Xu, LIU Jian, LI Hai-Liang, XIAO Ling. CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia,Series B, 2012, 32(1): 315-324.

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CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

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