Multi-Sink Solutions to the Self-Similar Euler Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911464056422400 |
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| author | Choi, Hyungjun Coiculescu, Matei P. |
| author_facet | Choi, Hyungjun Coiculescu, Matei P. |
| contents | We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than one stagnation point. These solutions are also homogeneous steady states of the Euler equations. In contrast, we prove that any homogeneous self-similar solution with bounded vorticity away from the origin necessarily admits only a single stagnation point, located at the origin. The solutions we construct develop velocity cusps along rays from the origin, and this allows for additional stagnation points of the pseudo-velocity field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Sink Solutions to the Self-Similar Euler Equations Choi, Hyungjun Coiculescu, Matei P. Analysis of PDEs Fluid Dynamics We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than one stagnation point. These solutions are also homogeneous steady states of the Euler equations. In contrast, we prove that any homogeneous self-similar solution with bounded vorticity away from the origin necessarily admits only a single stagnation point, located at the origin. The solutions we construct develop velocity cusps along rays from the origin, and this allows for additional stagnation points of the pseudo-velocity field. |
| title | Multi-Sink Solutions to the Self-Similar Euler Equations |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2602.15152 |