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arXiv · 2408.14662

A Classification Theorem for Steady Euler Flows

Tarek M. Elgindi·Yupei Huang·Ayman R. Said·Chunjing Xie
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Abstract

Fix a bounded, analytic, and simply connected domain $\Omega\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $\psi$ are either radial or solve a semi-linear elliptic equation of the form $\Delta \psi = F(\psi)$ with Dirichlet boundary conditions. In particular, if $\Omega$ is not a ball, then there exists a one to one correspondence between analytic steady states of the Euler equations and analytic solutions of equations of the form $\Delta \psi = F(\psi)$ with Dirichlet boundary conditions.

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Tarek M. Elgindi, Yupei Huang, Ayman R. Said, Chunjing Xie. 2024-08-26. A Classification Theorem for Steady Euler Flows. https://arxiv.org/abs/2408.14662

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