Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (5): 1195-1214.doi: 10.1007/s10473-020-0503-0

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ASYMPTOTIC STABILITY OF A VISCOUS CONTACT WAVE FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE

Lishuang PENG   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2019-10-17 Revised:2020-05-20 Online:2020-10-25 Published:2020-11-04
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11871341).

Abstract: 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 L2-energy methods.

Key words: reacting mixture, viscous contact wave, asymptotic stability, energy estimates

CLC Number: 

  • 35Q30
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