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arXiv · 2603.03666

On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations

Alexey Cheskidov·Hedong Hou
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Abstract

We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. We also establish uniqueness of stationary weak solutions in an endpoint critical space. Similar results are proved for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian in both Lebesgue and Besov spaces.

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Alexey Cheskidov, Hedong Hou. 2026-03-04. On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations. https://arxiv.org/abs/2603.03666

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