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Stability of viscous contact wave for compressible Navier-Stokes equations with a large initial perturbation

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Abstract

The viscous contact wave for the compressible Navier-Stokes equations has recently been shown to be asymptotically stable provided that all the L 2 norms of initial perturbations, their derivatives and/or anti-derivatives are small. The main purpose of this paper is to study the asymptotic stability and convergence rate of the viscous contact wave with a large initial perturbation. For this purpose, we introduce a positive number l in the construction of a smooth approximation of the contact discontinuity for the compressible Euler equations and then we make the quantity l to be sufficiently large in order to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. This makes for us to estimate the L 2 norms of the solution and its derivative for perturbation system without assuming that L 2 norms of the anti-derivatives and the derivatives of initial perturbations are small.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences, Pyong Yang, D.P.R. Korea

    Hakho Hong

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  1. Hakho Hong
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Correspondence to Hakho Hong.

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Supported by the CAS-TWAS postdoctoral fellowships (FR number: 3240223274) and AMSS in Chinese Academy of Sciences.

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Hong, H. Stability of viscous contact wave for compressible Navier-Stokes equations with a large initial perturbation. Acta Math. Appl. Sin. Engl. Ser. 31, 191–212 (2015). https://doi.org/10.1007/s10255-015-0460-x

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  • DOI: https://doi.org/10.1007/s10255-015-0460-x

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