Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction

Yuxi Hu; Reinhard Racke

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arXiv · 2509.22029

Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction

Yuxi Hu·Reinhard Racke

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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.

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Yuxi Hu, Reinhard Racke. 2025-09-26. Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction. https://arxiv.org/abs/2509.22029

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