Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations |
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Authors: | Feimin Huang Akitaka Matsumura Zhouping Xin |
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Institution: | (1) Institute of Applied Mathematics AMSS, Academia Sinica, China;(2) Department of Pure and Applied Mathematics Graduate School of Information Science and Technology, Osaka University, Japan;(3) The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong |
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Abstract: | 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. |
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