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

doi:10.1007/s10473-020-0503-0

Abstract

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

Lishuang PENG. ASYMPTOTIC STABILITY OF A VISCOUS CONTACT WAVE FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE[J].Acta mathematica scientia,Series B, 2020, 40(5): 1195-1214.

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