English

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}
}
R2 v1 2026-07-01T05:58:11.486Z