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arXiv · 2507.19443

Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension

Siddhant Agrawal·Neel Patel
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Abstract

We consider the Hele-Shaw problem with surface tension in an infinite domain. We prove the existence of a family of self-similar solutions. At $t=0$, these solutions have a corner of angle $\theta$ with $ 0 < |\theta - \pi| \ll 1$, and for $t>0$, the solutions are smooth.

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Siddhant Agrawal, Neel Patel. 2025-07-25. Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension. https://arxiv.org/abs/2507.19443

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