Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness

Fuente: arXiv
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Main Author: Li, Siran
Format: Preprint
Published: 2026
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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
id 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