NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY*

doi:10.1007/s10473-023-0515-7

Abstract

Abstract: In this paper, we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only, it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves, while the initial perturbation and the strength of rarefaction waves are suitably small.

Key words: rarefaction waves, reacting mixture, nonlinear stability, zero heat conductivity

CLC Number:

35Q30

Lishuang Peng, Yong Li. NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY^*[J].Acta mathematica scientia,Series A, 2023, 43(5): 2179-2203.

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NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY^*

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