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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17147 |
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| _version_ | 1866908341368782848 |
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| author | Xu, Xiangsheng |
| author_facet | Xu, Xiangsheng |
| contents | We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one whenever the initial velocity is divergence free and uniformly bounded with finite energy. Our results seem to have given a positive answer to the Navier-Stokes millennium problem proposed by the Clay Mathematical Institute. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions Xu, Xiangsheng Analysis of PDEs We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one whenever the initial velocity is divergence free and uniformly bounded with finite energy. Our results seem to have given a positive answer to the Navier-Stokes millennium problem proposed by the Clay Mathematical Institute. |
| title | Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17147 |