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

2025/09/26 by Hu, Yuxi, Racke, Reinhard
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.22029

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.

Citations

• Initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations
• Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations
• Global well-posedness and relaxation limit for relaxed compressible Navier-Stokes-Fourier equations in bounded domain
• The Cattaneo-Christov approximation of Fourier heat-conductive compressible fluids
• Blow-up of solutions for relaxed compressible Navier-Stokes equations

Related

• Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations
• On the steady compressible Navier-Stokes-Fourier system
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• Uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system in 3-D bounded domain
• Global existence of weak solutions to the compressible Navier-Stokes equations with temperature-depending viscosity coefficients