Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913069340295168 |
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| author | Li, Siran |
| author_facet | Li, Siran |
| contents | We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a constant depending only on the domain. This answers a problem raised in [D. Albritton, T. Barker, and C. Prange, J. Math. Fluid Mech. 25 (2023), Paper No. 49]. Our proof relies on a new slicing construction near the boundary of the domain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness Li, Siran Analysis of PDEs Fluid Dynamics We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a constant depending only on the domain. This answers a problem raised in [D. Albritton, T. Barker, and C. Prange, J. Math. Fluid Mech. 25 (2023), Paper No. 49]. Our proof relies on a new slicing construction near the boundary of the domain. |
| title | Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2604.25669 |