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arXiv 2602.03341math.AP
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平面 stationary Navier-Stokes 方程自相似解的局部特性

Local profiles of self-similar solutions of the planar stationary Navier--Stokes equations

Tongji University(同济大学);Keio University(庆应义塾大学);University of Chinese Academy of Sciences(中国科学院大学)

Ming Li, Linyu Peng, Ping Zhang, Xin Zhang

AI总结:

本文研究了平面 stationary Navier-Stokes 方程自相似解的局部特性,推导了径向和非径向解的显式局部特征。

摘要:

本文重新审视了在缩放对称下二维 stationary incompressible Navier-Stokes 方程的自相似解,也称为 Jeffery-Hamel 解。我们研究了在具有顶点在原点的锥形子域 Ω 内的光滑 Jeffery-Hamel 解的局部模式,不施加任何边界条件。对于径向 Jeffery-Hamel 解,我们得到了任意开角下 Ω 内的所有显式局部特征。在非径向情况下,我们证明了一些 Jeffery-Hamel 解可通过求解 Liénard 方程获得,并推导了新的显式局部特征,其可表示为 Weierstrass 椭圆函数的形式。

英文摘要:

In this paper, we revisit self-similar solutions of the two-dimensional stationary incompressible Navier-Stokes equations under scaling symmetries, also known as Jeffery-Hamel solutions. We investigate the local patterns of smooth Jeffery-Hamel solutions in a conical subdomain $Ω$ with vertex at the origin, without imposing any boundary conditions on $Ω$. For radial Jeffery-Hamel solutions, we obtain all the explicit local profiles in $Ω$ with arbitrary opening angles. In the non-radial case, we show that some Jeffery-Hamel solutions can be obtained via solving a Liénard equation, and we derive new explicit local profiles expressible in terms of Weierstrass elliptic functions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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