Potential flows away from stagnation in infinite cylinders
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915168411189248 |
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| author | Hamel, François Karakhanyan, Aram |
| author_facet | Hamel, François Karakhanyan, Aram |
| contents | Steady incompressible potential flows of an inviscid or viscous fluid are considered in infinite N-dimensional cylinders with tangential boundary conditions. We show that such flows, if away from stagnation, are constant and parallel to the direction of the cylinder. This means equivalently that a harmonic function whose gradient is bounded away from zero in an infinite cylinder with Neumann boundary conditions is an affine function. The proof of this rigidity result uses a combination of ODE and PDE arguments, respectively for the streamlines of the flow and the harmonic potential function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Potential flows away from stagnation in infinite cylinders Hamel, François Karakhanyan, Aram Analysis of PDEs Steady incompressible potential flows of an inviscid or viscous fluid are considered in infinite N-dimensional cylinders with tangential boundary conditions. We show that such flows, if away from stagnation, are constant and parallel to the direction of the cylinder. This means equivalently that a harmonic function whose gradient is bounded away from zero in an infinite cylinder with Neumann boundary conditions is an affine function. The proof of this rigidity result uses a combination of ODE and PDE arguments, respectively for the streamlines of the flow and the harmonic potential function. |
| title | Potential flows away from stagnation in infinite cylinders |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.02571 |