Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916852956921856 |
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| author | Hu, Yuxi Yuan, Mengran |
| author_facet | Hu, Yuxi Yuan, Mengran |
| contents | This paper studies an initial boundary value problem for the multidimensional hyperbolized compressible Navier-Stokes equations, in which the classical Newtonian law is replaced by the Maxwell law. We seek spherically symmetric solutions to the studied system in an exterior domain of a ball in $\mathbb R^3$, which are a system possessing a uniform characteristic boundary. First, we construct an approximate system featuring a non-characteristic boundary and establish its local well-posedness. Subsequently, by defining a suitable weighted energy functional and carefully handling boundary terms, we derive uniform a priori estimates, enabling the proof of uniform global existence. Leveraging these uniform estimates alongside standard compactness arguments, we establish the global well-posedness of the original system. Additionally, we rigorously justify the global relaxation limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations Hu, Yuxi Yuan, Mengran Analysis of PDEs This paper studies an initial boundary value problem for the multidimensional hyperbolized compressible Navier-Stokes equations, in which the classical Newtonian law is replaced by the Maxwell law. We seek spherically symmetric solutions to the studied system in an exterior domain of a ball in $\mathbb R^3$, which are a system possessing a uniform characteristic boundary. First, we construct an approximate system featuring a non-characteristic boundary and establish its local well-posedness. Subsequently, by defining a suitable weighted energy functional and carefully handling boundary terms, we derive uniform a priori estimates, enabling the proof of uniform global existence. Leveraging these uniform estimates alongside standard compactness arguments, we establish the global well-posedness of the original system. Additionally, we rigorously justify the global relaxation limit. |
| title | Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.15179 |