Global well-posedness of 3D inhomogenous incompressible Navier-Stokes equations with density-dependent viscosity
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916103897219072 |
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| author | Niu, Dongjuan Wang, Lu |
| author_facet | Niu, Dongjuan Wang, Lu |
| contents | The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent viscosity under the smallness assumption of initial velocity in the critical space $\dot{B}_{p,1}^{-1+\frac 3p}$ with $p\in ]1, 9/2]$. To the best of our knowledge, this is the first result about the global well-posedness for which one does not assume any smallness condition on the density when the initial density is far away from vacuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of 3D inhomogenous incompressible Navier-Stokes equations with density-dependent viscosity Niu, Dongjuan Wang, Lu Analysis of PDEs 35Q30, 76D03 The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent viscosity under the smallness assumption of initial velocity in the critical space $\dot{B}_{p,1}^{-1+\frac 3p}$ with $p\in ]1, 9/2]$. To the best of our knowledge, this is the first result about the global well-posedness for which one does not assume any smallness condition on the density when the initial density is far away from vacuum. |
| title | Global well-posedness of 3D inhomogenous incompressible Navier-Stokes equations with density-dependent viscosity |
| topic | Analysis of PDEs 35Q30, 76D03 |
| url | https://arxiv.org/abs/2401.13265 |