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arXiv · 2610.25531

Regularity of asymptotically axisymmetric Navier-Stokes flows with rotationally invariant curl of the force

Benjamin Ingimarson·Igor Kukavica·Qi Xu
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Abstract

We answer a question of Constantin, Ignatova, and Vicol concerning regularity of asymptotically axisymmetric solutions to the three-dimensional Navier-Stokes equations. For suitable weak solutions that are smooth before a terminal time and have a force uniformly bounded in $C_x^2$, we replace spatial analyticity of the force by rotational invariance of its curl. Under the same anisotropic Type II bounds on the angular mean and exact axial symmetry on a possibly collapsing core, the solution is axisymmetric on the entire cylinder and regular at the putative singular point. No time regularity or quantitative lower bound on the core radius is required. The proof combines unique continuation for linear Stokes systems with a Baire category argument and the axisymmetric regularity theorem due to Constantin, Ignatova, and Vicol.

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Benjamin Ingimarson, Igor Kukavica, Qi Xu. 2026-10-18. Regularity of asymptotically axisymmetric Navier-Stokes flows with rotationally invariant curl of the force. https://arxiv.org/abs/2610.25531

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