Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| author | Liao, Xian Zodji, Sagbo Marcel |
| author_facet | Liao, Xian Zodji, Sagbo Marcel |
| contents | We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as blocks, for \textit{less} regular initial data where the vacuum is permitted, the global-in-time well-posedness follows from the energy estimates and the propagated striated regularity of the density function, if the bulk viscosity coefficient is large enough in the two dimensional case. The global-in-time well-posedness holds also true in the three dimensional case, provided with large bulk viscosity coefficient together with small initial energy. This solves the density-patch problem in the exterior domain for the compressible model with $W^{2,p}$-Interfaces. Finally, the singular incompressible limit toward the inhomogenous incompressible model when the bulk viscosity coefficient tends to infinity is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density Liao, Xian Zodji, Sagbo Marcel Analysis of PDEs 35A01, 35A02, 35Q30, 35R35, 76N10 We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as blocks, for \textit{less} regular initial data where the vacuum is permitted, the global-in-time well-posedness follows from the energy estimates and the propagated striated regularity of the density function, if the bulk viscosity coefficient is large enough in the two dimensional case. The global-in-time well-posedness holds also true in the three dimensional case, provided with large bulk viscosity coefficient together with small initial energy. This solves the density-patch problem in the exterior domain for the compressible model with $W^{2,p}$-Interfaces. Finally, the singular incompressible limit toward the inhomogenous incompressible model when the bulk viscosity coefficient tends to infinity is obtained. |
| title | Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density |
| topic | Analysis of PDEs 35A01, 35A02, 35Q30, 35R35, 76N10 |
| url | https://arxiv.org/abs/2405.11900 |