Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913792456130560 |
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| author | Cao, Yue Jiang, Xun |
| author_facet | Cao, Yue Jiang, Xun |
| contents | This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature $θ$ in the form of $θ^ν$ with $ν>0$. Due to the appearance of the vacuum, the momentum equation are both degenerate in the time evolution and spatial dissipation, which makes the study on the well-posedness challenged. By establishing some new singular-weighted (negative powers of the density $ρ$) estimates of the solution, we establish the local-in-time well-posedness of the regular solution with far-field vacuum in terms of $ρ$, the velocity $u$ and the entropy $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity Cao, Yue Jiang, Xun Analysis of PDEs 35Q30, 35A09, 35A01, 35B40, 76N10 This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature $θ$ in the form of $θ^ν$ with $ν>0$. Due to the appearance of the vacuum, the momentum equation are both degenerate in the time evolution and spatial dissipation, which makes the study on the well-posedness challenged. By establishing some new singular-weighted (negative powers of the density $ρ$) estimates of the solution, we establish the local-in-time well-posedness of the regular solution with far-field vacuum in terms of $ρ$, the velocity $u$ and the entropy $S$. |
| title | Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity |
| topic | Analysis of PDEs 35Q30, 35A09, 35A01, 35B40, 76N10 |
| url | https://arxiv.org/abs/2504.10094 |