Approximation of the relaxed Euler system at the level of the compressible Navier-Stokes equations
Abstract
We study the global well-posedness of the Cauchy problem in ℝd, d≥2, for the relaxed compressible Euler system with a Maxwell-type constitutive law for the stress tensor. We show that the corresponding compressible Navier-Stokes solutions serve as both relaxation limits and large-time asymptotic profiles of the global relaxed Euler solutions constructed here. Given a Navier-Stokes background satisfying suitable boundedness and decay assumptions, we construct global smooth relaxed Euler solutions for each fixed α∈(0,1] and sufficiently small ε>0. Here, the background need not be small. After subtracting the stress initial layer, the approximation error is O(εα) uniformly in time. Under suitable additional conditions on the initial perturbations, this error decays in L2 faster than the decay of standard Navier-Stokes background, uniformly in ε, identifying the background solution as a large-time asymptotic profile. As an application, we obtain the corresponding small-data results using classical Navier-Stokes theory to verify the background assumptions.
Related
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- Uniform Decay for Ruggeri's Relaxed Navier-Stokes-Fourier Equations
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- Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition
BibTeX
@misc{chen2026approximation,
title = {{Approximation of the relaxed Euler system at the level of the compressible Navier-Stokes equations}},
author = {Hao Chen and Tao Wang and Junhao Zhang and Huijiang Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39552},
eprint = {2610.39552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39552},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Approximation of the relaxed Euler system at the level of the compressible Navier-Stokes equations
AU - Hao Chen
AU - Tao Wang
AU - Junhao Zhang
AU - Huijiang Zhao
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39552
UR - https://arxiv.org/abs/2610.39552
AB - We study the global well-posedness of the Cauchy problem in ℝ^d, d≥2, for the relaxed compressible Euler system with a Maxwell-type constitutive law for the stress tensor. We show that the corresponding compressible Navier-Stokes solutions serve as both relaxation limits and large-time asymptotic profiles of the global relaxed Euler solutions constructed here. Given a Navier-Stokes background satisfying suitable boundedness and decay assumptions, we construct global smooth relaxed Euler solutions for each fixed α∈(0,1] and sufficiently small ε>0. Here, the background need not be small. After subtracting the stress initial layer, the approximation error is O(ε^α) uniformly in time. Under suitable additional conditions on the initial perturbations, this error decays in L^2 faster than the decay of standard Navier-Stokes background, uniformly in ε, identifying the background solution as a large-time asymptotic profile. As an application, we obtain the corresponding small-data results using classical Navier-Stokes theory to verify the background assumptions.
ER -