Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction
Analysis of PDEs
2025-09-29 v1
Abstract
We study an initial boundary value problem for the 3-dimensional compressible Navier-Stokes equations with hyperbolic heat conduction, where the classical Fourier law is replaced by the Cattaneo-Christov constitutive relation. We focus on spherically symmetric solutions. We establish the existence of uniform global small solutions to the resulting system. Furthermore, based on uniform a priori estimates, we rigorously justify both the relaxation limit and the vanishing viscosity limit.
Keywords
Cite
@article{arxiv.2509.22029,
title = {Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction},
author = {Yuxi Hu and Reinhard Racke},
journal= {arXiv preprint arXiv:2509.22029},
year = {2025}
}