发表机构
Instituto de Matemáticas, Universidad de Valparaíso; School of Mathematics, Harbin Institute of Technology（瓦尔帕莱索大学数学研究所; 哈尔滨工业大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广了Chae-Wolf关于定常Navier-Stokes方程的Liouville型定理，证明其对数权重条件可扩展至更广泛的加权框架，包括迭代对数及非对数权重，从而在更一般的加权可积性条件下保证解的平凡性。
AI 中文摘要
在本文中，我们重新审视了Chae和Wolf在$\mathbb{R}^3$中关于定常Navier-Stokes方程的Liouville型定理[J. Differential Equations 261 (2016) 5541-5560]。我们证明他们对经典$L^{9/2}$条件的对数改进是一个更广泛的加权框架的一部分。更精确地说，我们证明，对于每一个正的、非递减的、有界的权重$\omega$，只要它在原点附近满足一个温和的增长条件，那么当$$ \int_{\mathbb{R}^3}|u(x)|^{9/2}\\,\omega(|u(x)|)\\,dx< +\infty $$时，解$u\in\dot H^1(\mathbb{R}^3)$必然是平凡的。这个结构条件包含了Chae和Wolf的对数权重，以及一系列迭代对数权重和（真正的）非对数例子，包括一个二进权重。我们的结果确定了更广泛的加权可积性条件类，在这些条件下，定常Navier-Stokes解的平凡性成立，并表明Chae-Wolf改进背后的机制并非本质上与特定的对数权重或单一对数尺度相关。
英文摘要
In this note, we revisit a Liouville-type theorem of Chae and Wolf for stationary Navier-Stokes equations in $\mathbb{R}^3$ [J. Differential Equations 261 (2016) 5541-5560]. We show that their logarithmic improvement of the classical $L^{9/2}$ condition is part of a substantially broader weighted framework. More precisely, we prove that a solution $u\in\dot H^1(\mathbb{R}^3)$ is necessarily trivial whenever $$ \int_{\mathbb{R}^3}|u(x)|^{9/2}\,ω(|u(x)|)\,dx< +\infty, $$ for every positive, nondecreasing and bounded weight $ω$ satisfying a mild growth condition near the origin. This structural condition encompasses the logarithmic weight due to Chae and Wolf, as well as a hierarchy of iterated-logarithmic weights and (genuinely) non-logarithmic examples, including a dyadic weight. Our result identifies a broader class of weighted integrability conditions under which the triviality of stationary Navier-Stokes solutions follows, and shows that the mechanism underlying the Chae-Wolf improvement is not intrinsically tied to a specific logarithmic weight or to a single logarithmic scale.
