Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations
Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations
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DOI：
10.1007/s00205-005-0380-7
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发表时间：
2006
影响因子：
2.5
通讯作者：
F. Huang;A. Matsumura;Z. Xin
中科院分区：
文献类型：
--
作者：
F. Huang;A. Matsumura;Z. Xin
本文研究了一维可压缩Navier-Stokes方程组解在接触间断处的大时间渐近性态，接触间断是可压缩Euler方程的基本波型之一.本文证明了在[24]中所介绍的意义下，这种弱接触间断是多变流体一维可压缩Navier-Stokes方程组的一种亚稳波型，即粘性接触波，它在任何有限时间间隔内对小的热传导逼近接触间断，然后在很长时间内远离接触间断，是非线性稳定的，具有一致的收敛速度，提供了初始多余质量为零。这一结果证明了一个精心组合的基本能量估计加权特征能量估计，它充分利用了粘性接触波的基本结构。
In this paper, we study the large-time asymptotic behavior of solutions of the one-dimensional compressible Navier-Stokes system toward a contact discontinuity, which is one of the basic wave patterns for the compressible Euler equations. It is proved that such a weak contact discontinuity is a metastable wave pattern, in the sense introduced in [24], for the 1-D compressible Navier-Stokes system for polytropic fluid by showing that a viscous contact wave, which approximates the contact discontinuity on any finite-time interval for small heat conduction and then runs away from it for large time, is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero. This result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate, which makes full use of the underlying structure of the viscous contact wave.