Non-unique $L^2$ solutions to the stationary Navier--Stokes equations on the whole plane

Mikihiro Fujii

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arXiv · 2608.17456

Non-unique $L^2$ solutions to the stationary Navier--Stokes equations on the whole plane

Mikihiro Fujii

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Abstract

We prove that, for a suitable small external force in $\dot H^{-2}(\mathbb R^2)$, the stationary Navier--Stokes equations on $\mathbb R^2$ admit multiple solutions in $L^2(\mathbb R^2)$.

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Mikihiro Fujii. 2026-08-18. Non-unique $L^2$ solutions to the stationary Navier--Stokes equations on the whole plane. https://arxiv.org/abs/2608.17456

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