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PreprintCC BY-NC-ND 4.0HAL

Solutions of the Riemann problem for the Self-Organized Hydrodynamics model

  • Christophe Berthon
  • Marie Compain
  • Carlos Parés
  • Ernesto Pimentel-García
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Abstract

The present paper is devoted to exhibit solutions of the Riemann problem for the Self-Organized Hydrodynamics model. The 2 × 2 system under consideration is strictly hyperbolic. With ambiguous non-conservative products, we adopt a non usual Generalized Rankine-Hugoniot jump condition to suitably define the shock wave solutions. This jump condition is obtained from the information given by the travelling wave solutions of the viscous extension of the system that involves the diffusion terms arising from the physics of the problem. We are then able to determine the simple waves of the non-conservative system studied here and we are able to construct some solutions of the Riemann problem of interest.

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Cite

BibTeXRIS
BibTeX
@misc{berthon2026solutions,
  title = {{Solutions of the Riemann problem for the Self-Organized Hydrodynamics model}},
  author = {Christophe Berthon and Marie Compain and Carlos Parés and Ernesto Pimentel-García},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37252},
  eprint = {2610.37252},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05839777v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Solutions of the Riemann problem for the Self-Organized Hydrodynamics model
AU  - Christophe Berthon
AU  - Marie Compain
AU  - Carlos Parés
AU  - Ernesto Pimentel-García
PY  - 2026
DA  - 2026/10/26
PB  - HAL
DO  - 10.48550/arxiv.2610.37252
UR  - https://hal.science/hal-05839777v1
AB  - The present paper is devoted to exhibit solutions of the Riemann problem for the Self-Organized Hydrodynamics model. The 2 × 2 system under consideration is strictly hyperbolic. With ambiguous non-conservative products, we adopt a non usual Generalized Rankine-Hugoniot jump condition to suitably define the shock wave solutions. This jump condition is obtained from the information given by the travelling wave solutions of the viscous extension of the system that involves the diffusion terms arising from the physics of the problem. We are then able to determine the simple waves of the non-conservative system studied here and we are able to construct some solutions of the Riemann problem of interest.
ER  -