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arXiv · 2411.14859

On a local solvability of the contact Muskat problem

Nataliya Vasylyeva
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Abstract

In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension of a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners $δ_{0}$ and $δ_{1}$ with fixed boundaries. Under suitable assumptions on the given data, the one-to-one local classical solvability of this problem is proved. We also describe the sufficient conditions on the data in the model which provide the existence of the "waiting time" phenomenon.

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Nataliya Vasylyeva. 2024-11-22. On a local solvability of the contact Muskat problem. https://arxiv.org/abs/2411.14859

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