2023/06/02 by Muhammed Ali Mehmood, Mehmood, Muhammed Ali
Mathematics · #35B25 #35Q35 #76T20 #90B20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2306.01379
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Aw-Rascle system in a one-dimensional domain with periodic boundary conditions, where the offset function is replaced by the gradient of the function ρnγ, where γ→ ∞. The resulting system resembles the 1D pressureless compressible Navier-Stokes system with a vanishing viscosity coefficient in the momentum equation and can be used to model traffic and suspension flows. We first prove the existence of a unique global-in-time classical solution for n fixed. Unlike the previous result for this system, we obtain global existence without needing to add any approximation terms to the system. This is by virtue of a n-uniform lower bound on the density which is attained by carrying out a maximum-principle argument on a suitable potential, Wn = ρn-1∂xwn. Then, we prove the convergence to a weak solution of a hybrid free-congested system as n → ∞, which is known as the hard-congestion model.