On the absence of anomalous dissipation for the Navier-Stokes equations with Navier boundary conditions: a sufficient condition
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911527179649024 |
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| author | Bardos, Claude Boutros, Daniel W. Titi, Edriss S. |
| author_facet | Bardos, Claude Boutros, Daniel W. Titi, Edriss S. |
| contents | We consider the three-dimensional incompressible Navier-Stokes equations in a bounded domain with Navier boundary conditions. We provide a sufficient condition for the absence of anomalous energy dissipation without making assumptions on the behaviour of the corresponding pressure near the boundary or the existence of a strong solution to the incompressible Euler equations with the same initial data. We establish our result by using our recent regularity results for the pressure corresponding to weak solutions of the incompressible Euler equations [Arch. Ration. Mech. Anal., 249 (2025), 28]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the absence of anomalous dissipation for the Navier-Stokes equations with Navier boundary conditions: a sufficient condition Bardos, Claude Boutros, Daniel W. Titi, Edriss S. Analysis of PDEs 35Q30 (primary), 35D30, 35Q31, 35Q35, 76D05, 76D10 (secondary) We consider the three-dimensional incompressible Navier-Stokes equations in a bounded domain with Navier boundary conditions. We provide a sufficient condition for the absence of anomalous energy dissipation without making assumptions on the behaviour of the corresponding pressure near the boundary or the existence of a strong solution to the incompressible Euler equations with the same initial data. We establish our result by using our recent regularity results for the pressure corresponding to weak solutions of the incompressible Euler equations [Arch. Ration. Mech. Anal., 249 (2025), 28]. |
| title | On the absence of anomalous dissipation for the Navier-Stokes equations with Navier boundary conditions: a sufficient condition |
| topic | Analysis of PDEs 35Q30 (primary), 35D30, 35Q31, 35Q35, 76D05, 76D10 (secondary) |
| url | https://arxiv.org/abs/2509.12432 |