On a Camassa-Holm type equation describing the dynamics of viscous fluid conduits
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910759935541248 |
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| author | Granero-Belinchón, Rafael |
| author_facet | Granero-Belinchón, Rafael |
| contents | In this note we derive a new nonlocal and nonlinear dispersive equations capturing the main dynamics of a circular interface separating a light, viscous fluid rising buoyantly through a heavy, more viscous, miscible fluid at small Reynolds numbers. This equation that we termed the $g-$model shares some common structure with the Camassa-Holm equation but has additional nonlocal effects. For this new PDE we study the well-posedness together with the existence of periodic traveling waves. Furthermore, we also show some numerical simulations suggesting the finite time singularity formation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Camassa-Holm type equation describing the dynamics of viscous fluid conduits Granero-Belinchón, Rafael Analysis of PDEs Fluid Dynamics In this note we derive a new nonlocal and nonlinear dispersive equations capturing the main dynamics of a circular interface separating a light, viscous fluid rising buoyantly through a heavy, more viscous, miscible fluid at small Reynolds numbers. This equation that we termed the $g-$model shares some common structure with the Camassa-Holm equation but has additional nonlocal effects. For this new PDE we study the well-posedness together with the existence of periodic traveling waves. Furthermore, we also show some numerical simulations suggesting the finite time singularity formation. |
| title | On a Camassa-Holm type equation describing the dynamics of viscous fluid conduits |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2412.17467 |