Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913455105114112 |
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| author | Huang, Xiangdi Li, Jiaxu Zhang, Rong |
| author_facet | Huang, Xiangdi Li, Jiaxu Zhang, Rong |
| contents | This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $μ(ρ)$ is a power function of the density ($μ(ρ)=μρ^α$ with $α>1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity Huang, Xiangdi Li, Jiaxu Zhang, Rong Analysis of PDEs 35Q35, 35B65, 76N10 This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $μ(ρ)$ is a power function of the density ($μ(ρ)=μρ^α$ with $α>1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions. |
| title | Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity |
| topic | Analysis of PDEs 35Q35, 35B65, 76N10 |
| url | https://arxiv.org/abs/2408.00333 |