Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915671261052928 |
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| author | Coiculescu, Matei P. Palasek, Stan |
| author_facet | Coiculescu, Matei P. Palasek, Stan |
| contents | We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space $BMO^{-1}$ from which there exist two distinct global solutions, both smooth for all $t>0$. One consequence of this construction is the sharpness of the celebrated small data global well-posedness result of Koch and Tataru. This appears to be the first example of non-uniqueness for the Navier-Stokes equations with data at the critical regularity. The proof is based on a non-uniqueness mechanism proposed by the second author in the context of the dyadic Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data Coiculescu, Matei P. Palasek, Stan Analysis of PDEs We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space $BMO^{-1}$ from which there exist two distinct global solutions, both smooth for all $t>0$. One consequence of this construction is the sharpness of the celebrated small data global well-posedness result of Koch and Tataru. This appears to be the first example of non-uniqueness for the Navier-Stokes equations with data at the critical regularity. The proof is based on a non-uniqueness mechanism proposed by the second author in the context of the dyadic Navier-Stokes equations. |
| title | Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.14699 |