Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients
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| Format: | Preprint |
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2025
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| _version_ | 1866914222655406080 |
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| author | Li, Yachun Lu, Peng Shang, Zhaoyang |
| author_facet | Li, Yachun Lu, Peng Shang, Zhaoyang |
| contents | It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations with temperature-dependent coefficients in the whole space. When the initial density and the initial temperature are linearly equivalent to some large constant states, we establish the first result on the global existence of large strong solution. Moreover, the optimal decay rates of the solution to its associated equilibrium are established when the initial data belong to $L^{p_0}(\mathbb{R}^3)$ for some $p_0\in[1,2]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients Li, Yachun Lu, Peng Shang, Zhaoyang Analysis of PDEs It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations with temperature-dependent coefficients in the whole space. When the initial density and the initial temperature are linearly equivalent to some large constant states, we establish the first result on the global existence of large strong solution. Moreover, the optimal decay rates of the solution to its associated equilibrium are established when the initial data belong to $L^{p_0}(\mathbb{R}^3)$ for some $p_0\in[1,2]$. |
| title | Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.06933 |