A geometric characterization of potential Navier-Stokes singularities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910786047180800 |
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| author | Lei, Zhen Ren, Xiao Tian, Gang |
| author_facet | Lei, Zhen Ren, Xiao Tian, Gang |
| contents | For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near a potential singularity, the directions of vorticity cannot avoid any great circle on the unit sphere. Our method, based on the control of local vorticity fluxes, is inspired by the classical Kelvin-Helmholtz law for ideal fluids and the Type I regularity theory for axisymmetric Navier-Stokes solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A geometric characterization of potential Navier-Stokes singularities Lei, Zhen Ren, Xiao Tian, Gang Analysis of PDEs For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near a potential singularity, the directions of vorticity cannot avoid any great circle on the unit sphere. Our method, based on the control of local vorticity fluxes, is inspired by the classical Kelvin-Helmholtz law for ideal fluids and the Type I regularity theory for axisymmetric Navier-Stokes solutions. |
| title | A geometric characterization of potential Navier-Stokes singularities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.08976 |