Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Soft congestion approximation to the one-dimensional constrained Euler equations

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02624318
Contributor : Charlotte Perrin <>
Submitted on : Tuesday, May 26, 2020 - 11:16:04 AM
Last modification on : Thursday, June 11, 2020 - 4:38:53 AM

Files

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02624318, version 1

Citation

Roberta Bianchini, Charlotte Perrin. Soft congestion approximation to the one-dimensional constrained Euler equations. 2020. ⟨hal-02624318⟩

Share

Metrics

Record views

33

Files downloads

14