Well-posedness of the 3-D compressible Navier-Stokes equations with density-dependent viscosities in exterior domains with far-field vacuum
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914187721048064 |
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| author | Liu, Hairong Zhong, Hua |
| author_facet | Liu, Hairong Zhong, Hua |
| contents | This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity coefficients depend on the density in a power law ($ρ^δ$ with $0<δ<1$) and Navier-slip boundary condition on the velocity is imposed, base on a reformulation of the problem using new variables to handle the degeneracy near vacuum, we establish the local well-posedness of regular solutions with far-field vacuum in inhomogeneous Sobolev spaces. Compared to the Cauchy problem, the initial-boundary value problem requires establishing non-standard weighted estimates and handling the unavailability of boundary conditions for higher-order terms. Our approach addresses these challenges via the conormal space technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the 3-D compressible Navier-Stokes equations with density-dependent viscosities in exterior domains with far-field vacuum Liu, Hairong Zhong, Hua Analysis of PDEs This paper investigates the local existence and uniqueness of strong solutions to the three-dimensional compressible Navier-Stokes equations with density-dependent viscosities in exterior domains. When both the shear and bulk viscosity coefficients depend on the density in a power law ($ρ^δ$ with $0<δ<1$) and Navier-slip boundary condition on the velocity is imposed, base on a reformulation of the problem using new variables to handle the degeneracy near vacuum, we establish the local well-posedness of regular solutions with far-field vacuum in inhomogeneous Sobolev spaces. Compared to the Cauchy problem, the initial-boundary value problem requires establishing non-standard weighted estimates and handling the unavailability of boundary conditions for higher-order terms. Our approach addresses these challenges via the conormal space technique. |
| title | Well-posedness of the 3-D compressible Navier-Stokes equations with density-dependent viscosities in exterior domains with far-field vacuum |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.07614 |