Global existence of large solutions to 3-D incompressible Navier-Stokes system
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917355625381888 |
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| author | Ru, Shaolei |
| author_facet | Ru, Shaolei |
| contents | This paper proves that the 3-D Navier-Stokes system has a unique global solution under an assumpution on the initial data. That allow the data to be arbitrarily large in the scale invariant space \dot{B}_{\infty,\infty}^{-1}, which contains all the known spaces in which there is a global solution for small data. In particular, this work extends the result of global well-posedness for the "ill-prepared" case in [6] to the full space \mathbb{R}^{3}(in [6] the fluid evolves in domain \mathbb{T}^{2}\times\mathbb{R}) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18308 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence of large solutions to 3-D incompressible Navier-Stokes system Ru, Shaolei Analysis of PDEs This paper proves that the 3-D Navier-Stokes system has a unique global solution under an assumpution on the initial data. That allow the data to be arbitrarily large in the scale invariant space \dot{B}_{\infty,\infty}^{-1}, which contains all the known spaces in which there is a global solution for small data. In particular, this work extends the result of global well-posedness for the "ill-prepared" case in [6] to the full space \mathbb{R}^{3}(in [6] the fluid evolves in domain \mathbb{T}^{2}\times\mathbb{R}) |
| title | Global existence of large solutions to 3-D incompressible Navier-Stokes system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.18308 |