Bifurcations of viscous shear flows in a strip
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916995366125568 |
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| author | Dongfen, Bian Emmanuel, Grenier Mariana, Haragus |
| author_facet | Dongfen, Bian Emmanuel, Grenier Mariana, Haragus |
| contents | It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this article, under a natural spectral assumption which is satisfied for convex or concave analytic flows, we prove that shear flows undergo a Hopf bifurcation near their upper marginal stability curve. In particular, near this curve, there exist solutions which are periodic in $t$ and $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcations of viscous shear flows in a strip Dongfen, Bian Emmanuel, Grenier Mariana, Haragus Analysis of PDEs 35Q30, 35B32 It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this article, under a natural spectral assumption which is satisfied for convex or concave analytic flows, we prove that shear flows undergo a Hopf bifurcation near their upper marginal stability curve. In particular, near this curve, there exist solutions which are periodic in $t$ and $x$. |
| title | Bifurcations of viscous shear flows in a strip |
| topic | Analysis of PDEs 35Q30, 35B32 |
| url | https://arxiv.org/abs/2501.02202 |