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

Yuxi Hu; Yachun Li

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arXiv · 2508.01634

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

Yuxi Hu·Yachun Li

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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.

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Yuxi Hu, Yachun Li. 2025-08-03. Initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations. https://arxiv.org/abs/2508.01634

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