On spiral steady flows for the Couette-Taylor problem
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912945516052480 |
|---|---|
| author | Bocchi, Edoardo Gazzola, Filippo Hidalgo-Torné, Antonio |
| author_facet | Bocchi, Edoardo Gazzola, Filippo Hidalgo-Torné, Antonio |
| contents | We investigate the Couette-Taylor problem for a steady incompressible viscous fluid in a 3D cylindrical annulus, where one of the two cylinders is still, under both Dirichlet and boundary conditions involving the vorticity that naturally appear in the weak formulation. The outcome of this study is twofold. First, we explicitly determine all the solutions with a specific geometric \emph{partial invariance}, which coincide with the so-called spiral Poiseuille or Poiseuille-Couette flows depending on the boundary conditions. Second, for small boundary data, we provide stability of such solutions, that is, no steady finite-energy perturbations are admissible. To achieve this result in presence of vorticity boundary conditions, we find a substantial analytical difference depending on which cylinder is still. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05401 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On spiral steady flows for the Couette-Taylor problem Bocchi, Edoardo Gazzola, Filippo Hidalgo-Torné, Antonio Analysis of PDEs 35Q30, 76D03, 35B06, 35B53, 34B24 We investigate the Couette-Taylor problem for a steady incompressible viscous fluid in a 3D cylindrical annulus, where one of the two cylinders is still, under both Dirichlet and boundary conditions involving the vorticity that naturally appear in the weak formulation. The outcome of this study is twofold. First, we explicitly determine all the solutions with a specific geometric \emph{partial invariance}, which coincide with the so-called spiral Poiseuille or Poiseuille-Couette flows depending on the boundary conditions. Second, for small boundary data, we provide stability of such solutions, that is, no steady finite-energy perturbations are admissible. To achieve this result in presence of vorticity boundary conditions, we find a substantial analytical difference depending on which cylinder is still. |
| title | On spiral steady flows for the Couette-Taylor problem |
| topic | Analysis of PDEs 35Q30, 76D03, 35B06, 35B53, 34B24 |
| url | https://arxiv.org/abs/2603.05401 |