On the weak solutions to the navier-Stokes equations: a possible gap related to the energy equality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908693816147968 |
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| author | Maremonti, Paolo |
| author_facet | Maremonti, Paolo |
| contents | It is well known that a Leray-Hopf weak solution enjoys an energy inequality. Here, we investigate the energy equality related to a suitable weak solution to the Navier-Stokes initial boundary value problem. The term suitable is meant in the sense that for our goals we achieve a weak solution whose existence is based as limit of solutions to the mollified Navier-Stokes system. In the case of a weak regularity of the solution, our results justify the possible gap for the energy equality in terms of "kinetic energy". However, if there is a sufficient regularity, e.g., like the continuity of the L2-norm of the weak solution, then the energy equality holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the weak solutions to the navier-Stokes equations: a possible gap related to the energy equality Maremonti, Paolo Mathematical Physics It is well known that a Leray-Hopf weak solution enjoys an energy inequality. Here, we investigate the energy equality related to a suitable weak solution to the Navier-Stokes initial boundary value problem. The term suitable is meant in the sense that for our goals we achieve a weak solution whose existence is based as limit of solutions to the mollified Navier-Stokes system. In the case of a weak regularity of the solution, our results justify the possible gap for the energy equality in terms of "kinetic energy". However, if there is a sufficient regularity, e.g., like the continuity of the L2-norm of the weak solution, then the energy equality holds. |
| title | On the weak solutions to the navier-Stokes equations: a possible gap related to the energy equality |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.04654 |