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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15598 |
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| _version_ | 1866910912251691008 |
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| author | Wang, Guodong |
| author_facet | Wang, Guodong |
| contents | We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of a class of exact solutions of the incompressible Euler equation in a disk Wang, Guodong Analysis of PDEs We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument. |
| title | Stability of a class of exact solutions of the incompressible Euler equation in a disk |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.15598 |