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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.18523 |
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| _version_ | 1866916707695591424 |
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| author | Elgindi, Tarek Filho, Milton Lopes Lopes, Helena Nussenzveig |
| author_facet | Elgindi, Tarek Filho, Milton Lopes Lopes, Helena Nussenzveig |
| contents | A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with an arbitrary non-negative measure plus an integrable function as initial vorticity and square-integrable initial velocity. Our result applies to flows with forcing and provides an explicit estimate for the dissipation at small viscosity. The proof relies on a new refinement of a classical inequality due to J. Nash. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of anomalous dissipation for vortex sheets Elgindi, Tarek Filho, Milton Lopes Lopes, Helena Nussenzveig Analysis of PDEs 35Q30, 35Q35, 76D05 A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with an arbitrary non-negative measure plus an integrable function as initial vorticity and square-integrable initial velocity. Our result applies to flows with forcing and provides an explicit estimate for the dissipation at small viscosity. The proof relies on a new refinement of a classical inequality due to J. Nash. |
| title | Absence of anomalous dissipation for vortex sheets |
| topic | Analysis of PDEs 35Q30, 35Q35, 76D05 |
| url | https://arxiv.org/abs/2504.18523 |