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A Classification Theorem for Steady Euler Flows by Elgindi, Tarek M.; Huang, Yupei; Said, Ayman R.; Xie, Chunjing is a scholarly article available to read on EtoBox.

What is A Classification Theorem for Steady Euler Flows about?

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.

Author

Elgindi, Tarek M.; Huang, Yupei; Said, Ayman R.; Xie, Chunjing

Published

2024

Language

EN