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arXiv · 2412.17467

On a Camassa-Holm type equation describing the dynamics of viscous fluid conduits

Rafael Granero-Belinchón
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Abstract

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.

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Rafael Granero-Belinchón. 2024-12-23. On a Camassa-Holm type equation describing the dynamics of viscous fluid conduits. https://arxiv.org/abs/2412.17467

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