Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913548145262592 |
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| author | Li, Jiaxu Mei, Yu Zhang, Rong |
| author_facet | Li, Jiaxu Mei, Yu Zhang, Rong |
| contents | This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $μ(ρ)$ is a power function of the density with the power larger than $1$, that is $μ(ρ)=μρ^α$ with $α>1$, it is proved that the system exists a unique global strong solution as long as the initial density is sufficiently large and $L^3$-norm of the derivative of the initial director is sufficiently small. This is the first result concerning the global strong solution for three-dimensional inhomogeneous liquid crystal flows without smallness of velocity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity Li, Jiaxu Mei, Yu Zhang, Rong Analysis of PDEs 35Q30, 35Q35, 76A15, This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $μ(ρ)$ is a power function of the density with the power larger than $1$, that is $μ(ρ)=μρ^α$ with $α>1$, it is proved that the system exists a unique global strong solution as long as the initial density is sufficiently large and $L^3$-norm of the derivative of the initial director is sufficiently small. This is the first result concerning the global strong solution for three-dimensional inhomogeneous liquid crystal flows without smallness of velocity. |
| title | Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity |
| topic | Analysis of PDEs 35Q30, 35Q35, 76A15, |
| url | https://arxiv.org/abs/2410.11881 |