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arXiv · 2602.12666

Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions

Shijun Liao·Shijie Qin
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Abstract

Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit distinct global solutions from almost the same initial conditions whose difference is very small, i.e. even at the order $10^{-40}$ of magnitude. Hopefully these examples could provide some enlightenments for the uniqueness and existence of Navier-Stokes equations, which are related to one Millennium Prize Problem of Clay Institute.

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BibTeXRIS

Shijun Liao, Shijie Qin. 2026-02-13. Non-uniqueness of smooth solutions of the Navier-Stokes equations from almost the same initial conditions. https://arxiv.org/abs/2602.12666

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