Regular solutions to the dissipative Aw-Rascle system

2024/11/05 by Nilasis Chaudhuri, Chaudhuri, Nilasis, Tomasz Piasecki +3 · 1 citation
Physics and Astronomy · #35M10 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2411.03024

openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the local-in-time existence of regular solutions to dissipative Aw-Rascle system with the offset equal to gradient of some increasing and regular function of density. It is a mixed degenerate parabolic-hyperbolic hydrodynamic model, and we extend the techniques previously developed for compressible Navier-Stokes equations to show the well-posedness of the system in the L₂-L₂ setting. We also discuss relevant existence results for offset involving singular or nonlocal functions of density.

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• Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw--Rascle--Zhang model of collective behaviour

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