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arXiv · 2605.05555

Notes on Liouville-type theorems for the 3D stationary Navier-Stokes equations

Hongling Jiang·Jianfeng Sun·Gastón Vergara-Hermosilla·Jihong Zhao
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Abstract

In \cite{CV23}, Chamorro and Vergara-Hermosilla established several Liouville-type theorems to the Navier-Stokes equations in the framework of the variable Lebesgue spaces. These results may allow the variable exponent $p(\cdot)$ beyond the range of $[3,\frac{9}{2}]$ in some non-negligible regions in $\mathbb{R}^3$. In this paper we find two new non-negligible regions, in which the Liouville-type theorems still hold under some assumptions imposed on $p(\cdot)$ in these regions. Our results can be regarded as the generalization of the results in \cite{CV23}.

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Hongling Jiang, Jianfeng Sun, Gastón Vergara-Hermosilla, Jihong Zhao. 2026-05-07. Notes on Liouville-type theorems for the 3D stationary Navier-Stokes equations. https://arxiv.org/abs/2605.05555

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