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arXiv · 2404.10972

Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions

Russell Schwab·Son Tu·Olga Turanova
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Abstract

In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravity). We prove global well-posedness for the corresponding Hamilton-Jacobi-Bellmann equation with bounded, uniformly continuous initial data, in all dimensions.

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Russell Schwab, Son Tu, Olga Turanova. 2024-04-17. Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions. https://arxiv.org/abs/2404.10972

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