Asymptotic stability of contact waves for the compressible Navier–Stokes equations

Abstract

In this article, we study the large-time asymptotic behaviour of contact wave for the Cauchy problem of one-dimensional compressible Navier–Stokes equations with zero viscosity. When the Riemann problem for the Euler system admits a contact discontinuity solution, we can construct a 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, and prove that it is nonlinearly stable provided that the strength of contact discontinuity and the perturbation of the initial data are suitably small.

Keywords:

• stability
• contact wave
• compressible Navier–Stokes equations

AMS Subject Classifications::

• 35M30
• 35Q30

Acknowledgements

The author is supported by the National Natural Science Foundation of China (Nos. 11101162, 11071086). And the author thanks Prof. Xie Feng for the motivation of the problem.