Subcritical bifurcations of shear flows
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908870331334656 |
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| author | Bian, Dongfen Dai, Shouyi Grenier, Emmanuel |
| author_facet | Bian, Dongfen Dai, Shouyi Grenier, Emmanuel |
| contents | It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $ν$ is small enough, provided the horizontal wave number $α$ lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subcritical bifurcations of shear flows Bian, Dongfen Dai, Shouyi Grenier, Emmanuel Analysis of PDEs 76D05 35B32 76E99 It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $ν$ is small enough, provided the horizontal wave number $α$ lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical. |
| title | Subcritical bifurcations of shear flows |
| topic | Analysis of PDEs 76D05 35B32 76E99 |
| url | https://arxiv.org/abs/2603.06322 |