Global three-dimensional subsonic Euler flows past an axisymmetric obstacle with large vorticity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914352336994304 |
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| author | Wang, Dehua Wang, Tian-Yi Wang, Weiqiang |
| author_facet | Wang, Dehua Wang, Tian-Yi Wang, Weiqiang |
| contents | In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic Euler flow exists provided that the upstream density exceeds a critical threshold. The non-degeneracy of the axial velocity is rigorously established by combining the strong maximum principle with a refined continuity argument. The asymptotic behavior of the flow is obtained from uniform integral estimates for the difference between the flow and the upstream state. In addition, this result accommodates flows with large vorticity under a structural condition, thereby differing from previous results in the two-dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global three-dimensional subsonic Euler flows past an axisymmetric obstacle with large vorticity Wang, Dehua Wang, Tian-Yi Wang, Weiqiang Analysis of PDEs 35Q31, 35M30, 76N10, 76G25, 35B40 In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic Euler flow exists provided that the upstream density exceeds a critical threshold. The non-degeneracy of the axial velocity is rigorously established by combining the strong maximum principle with a refined continuity argument. The asymptotic behavior of the flow is obtained from uniform integral estimates for the difference between the flow and the upstream state. In addition, this result accommodates flows with large vorticity under a structural condition, thereby differing from previous results in the two-dimensional case. |
| title | Global three-dimensional subsonic Euler flows past an axisymmetric obstacle with large vorticity |
| topic | Analysis of PDEs 35Q31, 35M30, 76N10, 76G25, 35B40 |
| url | https://arxiv.org/abs/2602.22598 |