Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.14662 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909983869763584 |
|---|---|
| author | Elgindi, Tarek M. Huang, Yupei Said, Ayman R. Xie, Chunjing |
| author_facet | Elgindi, Tarek M. Huang, Yupei Said, Ayman R. Xie, Chunjing |
| contents | Fix a bounded, analytic, and simply connected domain $Ω\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $ψ$ are either radial or solve a semi-linear elliptic equation of the form $Δψ= F(ψ)$ with Dirichlet boundary conditions. In particular, if $Ω$ 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 $Δψ= F(ψ)$ with Dirichlet boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Classification Theorem for Steady Euler Flows Elgindi, Tarek M. Huang, Yupei Said, Ayman R. Xie, Chunjing Analysis of PDEs Fix a bounded, analytic, and simply connected domain $Ω\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $ψ$ are either radial or solve a semi-linear elliptic equation of the form $Δψ= F(ψ)$ with Dirichlet boundary conditions. In particular, if $Ω$ 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 $Δψ= F(ψ)$ with Dirichlet boundary conditions. |
| title | A Classification Theorem for Steady Euler Flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.14662 |