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

TL;DR

This paper studies a one-dimensional hyperbolic compressible Navier-Stokes initial boundary value problem, establishing global smooth solutions and analyzing the relaxation limit through coordinate transformation and approximation methods.

Contribution

It introduces a novel approach using Lagrangian coordinates and approximate systems to prove global existence and relaxation limits for the hyperbolic Navier-Stokes equations.

Findings

Established global smooth solutions for the problem.

Derived the global relaxation limit.

Developed a method to handle characteristic boundaries.

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.