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Article Dans Une Revue Nonlinearity Année : 2021

Soft congestion approximation to the one-dimensional constrained Euler equations

Résumé

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded weak solutions by means of a viscous regularization and refined compensated compactness arguments. Second, we investigate the smooth setting by providing a detailed description of the impact of the singular pressure on the breakdown of the solutions. In this smooth framework, we rigorously justify the singular limit towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.
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Dates et versions

hal-02624318 , version 1 (26-05-2020)
hal-02624318 , version 2 (30-09-2021)

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Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

  • HAL Id : hal-02624318 , version 2

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Roberta Bianchini, Charlotte Perrin. Soft congestion approximation to the one-dimensional constrained Euler equations. Nonlinearity, In press. ⟨hal-02624318v2⟩
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