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

Ming Li; Linyu Peng; Ping Zhang; Xin Zhang

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arXiv · 2602.03341

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

Ming Li·Linyu Peng·Ping Zhang·Xin Zhang

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Abstract

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 $\Omega$ with vertex at the origin, without imposing any boundary conditions on $\Omega$. For radial Jeffery-Hamel solutions, we obtain all the explicit local profiles in $\Omega$ with arbitrary opening angles. In the non-radial case, we show that some Jeffery-Hamel solutions can be obtained via solving a Li\'enard equation, and we derive new explicit local profiles expressible in terms of Weierstrass elliptic functions.

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BibTeX RIS

Ming Li, Linyu Peng, Ping Zhang, Xin Zhang. 2026-02-03. Local profiles of self-similar solutions of the planar stationary Navier--Stokes equations. https://arxiv.org/abs/2602.03341

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