Existence and stability of partially congested propagation fronts in a one-dimensional Navier-Stokes model

Abstract : In this paper, we analyze the behavior of viscous shock profiles of one-dimensional compressible Navier-Stokes equations with a singular pressure law which encodes the effects of congestion. As the intensity of the singular pressure tends to 0, we show the convergence of these profiles towards free-congested traveling front solutions of a two-phase compressible-incompressible Navier-Stokes system and we provide a refined description of the profiles in the vicinity of the transition between the free domain and the congested domain. In the second part of the paper, we prove that the profiles are asymptotically nonlinearly stable under small perturbations with zero integral, and we quantify the size of the admissible perturbations in terms of the intensity of the singular pressure.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-02010404
Contributeur : Anne-Laure Dalibard <>
Soumis le : jeudi 7 février 2019 - 10:41:36
Dernière modification le : samedi 16 mars 2019 - 01:30:06

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DP-congestion-soumission.pdf
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  • HAL Id : hal-02010404, version 1
  • ARXIV : 1902.02982

Citation

Anne-Laure Dalibard, Charlotte Perrin. Existence and stability of partially congested propagation fronts in a one-dimensional Navier-Stokes model. 2019. 〈hal-02010404〉

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