Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916971611684864 |
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| author | Hu, Yuxi Racke, Reinhard |
| author_facet | Hu, Yuxi Racke, Reinhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction Hu, Yuxi Racke, Reinhard Analysis of PDEs 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. |
| title | Initial boundary value problems for 3-d Navier-Stokes equations with hyperbolic heat conduction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.22029 |