Global well-posedness and optimal time-decay of 3D full compressible Navier-Stokes system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912282322141184 |
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| author | Huo, Wenwen Zhang, Chao |
| author_facet | Huo, Wenwen Zhang, Chao |
| contents | In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases. First of all, we study the global well-posedness of the Cauchy problem to the system when the initial data is small enough. Secondly, we show the optimal decay rates of the higher-order spatial derivatives of the $\dot{H}^{-s}$ $\left(0\leq s<\frac{3}{2}\right)$ negative Sobolev norms. Finally, under the assumption that the initial data is bounded in $L^{1}$-norm, we establish the upper and lower bounds of the optimal decay rates for the classical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and optimal time-decay of 3D full compressible Navier-Stokes system Huo, Wenwen Zhang, Chao Analysis of PDEs In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases. First of all, we study the global well-posedness of the Cauchy problem to the system when the initial data is small enough. Secondly, we show the optimal decay rates of the higher-order spatial derivatives of the $\dot{H}^{-s}$ $\left(0\leq s<\frac{3}{2}\right)$ negative Sobolev norms. Finally, under the assumption that the initial data is bounded in $L^{1}$-norm, we establish the upper and lower bounds of the optimal decay rates for the classical solutions. |
| title | Global well-posedness and optimal time-decay of 3D full compressible Navier-Stokes system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.14808 |