数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 934-952.doi: 10.1016/S0252-9602(11)60287-7

• 论文 • 上一篇    下一篇

INTERFACE BEHAVIOR OF COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS AND VACUM

郭真华, 贺文   

  1. Center for Nonlinear Studies and Department of Mathematics, Northwest University, Xi'an 710069, China
  • 收稿日期:2009-06-19 出版日期:2011-05-20 发布日期:2011-05-20
  • 基金资助:

    Supported in part by the NSFC (10771170).

INTERFACE BEHAVIOR OF COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS AND VACUM

 GUO Zhen-Hua, HE Wen   

  1. Center for Nonlinear Studies and Department of Mathematics, Northwest University, Xi'an 710069, China
  • Received:2009-06-19 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    Supported in part by the NSFC (10771170).

摘要:

In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang  [12]  to the jump boundary conditions case.

关键词: interface, Navier-Stokes equations, vacuum

Abstract:

In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang  [12]  to the jump boundary conditions case.

Key words: interface, Navier-Stokes equations, vacuum

中图分类号: 

  • 35Q10