The structure of weak solutions to the Navier-Stokes equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908476627746816 |
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| author | Bradshaw, Zachary Kukavica, Igor |
| author_facet | Bradshaw, Zachary Kukavica, Igor |
| contents | The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local pressure expansion. We prove that every weak solution in a parabolic uniformly local $L^2$ class can be obtained as a transgalilean transformation of a solution satisfying the local pressure expansion in a distributional sense. This gives a powerful representation theorem for a large class of solutions. We use this structure to obtain a sufficient condition for the local pressure expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The structure of weak solutions to the Navier-Stokes equations Bradshaw, Zachary Kukavica, Igor Analysis of PDEs The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local pressure expansion. We prove that every weak solution in a parabolic uniformly local $L^2$ class can be obtained as a transgalilean transformation of a solution satisfying the local pressure expansion in a distributional sense. This gives a powerful representation theorem for a large class of solutions. We use this structure to obtain a sufficient condition for the local pressure expansion. |
| title | The structure of weak solutions to the Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.01009 |