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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.19032 |
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| _version_ | 1866913060426350592 |
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| author | Xing, Yuanyuan Zhang, Zihao |
| author_facet | Xing, Yuanyuan Zhang, Zihao |
| contents | This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove
the existence of radially symmetric subsonic solutions to the steady Euler-Poisson system. We then investigate the structural stability of these background subsonic flows under perturbations of suitable boundary conditions, and establish the existence and uniqueness of smooth subsonic Euler-Poisson flows with nonzero vorticity. The solution shares the same regularity for the velocity, the pressure, the entropy and the electric potential. The deformation-curl-Poisson decomposition is utilized to reformulate the steady Euler-Poisson system as a deformation-curl-Poisson system together with several transport equations. The key point lies on the analysis of the well-posedness of the boundary value problem for the associated linearized elliptic system, which is established by using a special structure of the system to derive a priori estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles Xing, Yuanyuan Zhang, Zihao Analysis of PDEs This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions to the steady Euler-Poisson system. We then investigate the structural stability of these background subsonic flows under perturbations of suitable boundary conditions, and establish the existence and uniqueness of smooth subsonic Euler-Poisson flows with nonzero vorticity. The solution shares the same regularity for the velocity, the pressure, the entropy and the electric potential. The deformation-curl-Poisson decomposition is utilized to reformulate the steady Euler-Poisson system as a deformation-curl-Poisson system together with several transport equations. The key point lies on the analysis of the well-posedness of the boundary value problem for the associated linearized elliptic system, which is established by using a special structure of the system to derive a priori estimates. |
| title | Subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.19032 |