Initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations

2025/08/03 by Yuxi Hu, Hu, Yuxi, Yachun Li +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.01634

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform characteristic boundary. By constructing an approximate system with non-characteristic boundary, we get a uniform global smooth solutions and obtain a global solution of the original problem by passing to a limit. Moreover, the global relaxation limit is also obtained.

Citations

• Formation of Singularities in Solutions to Ruggeri's Hyperbolic Navier-Stokes Equations
• Blow-up of solutions to relaxed compressible Navier-Stokes equations in divergence form
• A Galilei Invariant Version of Yong's Model

Cited by

• Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction

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