Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915799405428736 |
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| author | Liao, Shijun Qin, Shijie |
| author_facet | Liao, Shijun Qin, Shijie |
| contents | Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit distinct global solutions from almost the same initial conditions whose difference is very small, i.e. even at the order $10^{-40}$ of magnitude. Hopefully these examples could provide some enlightenments for the uniqueness and existence of Navier-Stokes equations, which are related to one Millennium Prize Problem of Clay Institute. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions Liao, Shijun Qin, Shijie Analysis of PDEs Numerical Analysis Chaotic Dynamics Computational Physics Fluid Dynamics Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit distinct global solutions from almost the same initial conditions whose difference is very small, i.e. even at the order $10^{-40}$ of magnitude. Hopefully these examples could provide some enlightenments for the uniqueness and existence of Navier-Stokes equations, which are related to one Millennium Prize Problem of Clay Institute. |
| title | Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions |
| topic | Analysis of PDEs Numerical Analysis Chaotic Dynamics Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2602.12666 |