Asymptotic Stability of a Viscous Contact Wave for the One-Dimensional Compressible Navier-Stokes Equations for a Reacting Mixture

We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which...

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Bibliographic Details
Published in:Acta mathematica scientia 2020-09, Vol.40 (5), p.1195-1214
Main Author: Peng, Lishuang
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable, provided the strength of contact discontinuity and the initial perturbation are suitably small. We apply the approach introduced in Huang, Li and Matsumura (2010) [ 1 ] and the elementary L 2 -energy methods.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-020-0503-0