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<p>In this paper, we investigate the asymptotic stability and convergence rate of the viscous contact wave under a large initial perturbation for the Cauchy problem to the compressible Navier–Stokes equations with a reacting mixture in one dimension provided that the strength of the viscous contact wave is sufficiently small. To this end, when we construct a smooth approximation to the contact discontinuity of the compressible Euler equations, a positive number <i>l</i> needs to be introduced. Then we make the quantity <i>l</i> large enough to control the growth induced by the nonlinearity of the system and the interaction of waves from different families.</p>

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Stability of viscous contact wave for compressible Navier–Stokes equations for a reacting mixture with a large initial perturbation

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Lishuang Peng,
  • Yong Li

摘要

In this paper, we investigate the asymptotic stability and convergence rate of the viscous contact wave under a large initial perturbation for the Cauchy problem to the compressible Navier–Stokes equations with a reacting mixture in one dimension provided that the strength of the viscous contact wave is sufficiently small. To this end, when we construct a smooth approximation to the contact discontinuity of the compressible Euler equations, a positive number l needs to be introduced. Then we make the quantity l large enough to control the growth induced by the nonlinearity of the system and the interaction of waves from different families.