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

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arxiv 2404.10972 v4 pith:4EWXUXI4 submitted 2024-04-17 math.AP

Russell Schwab , Son Tu , Olga Turanova This is my paper · ORCID
classification math.AP
keywords dimensionsequationmuskatone-phaseproblemsolutionsviscositywell-posedness
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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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  1. Well-posedness of a Hele-Shaw problem in general dimensions

    math.AP 2026-07 conditional novelty 7.0 of 10

    Comparison, maximal-flow existence, and generic uniqueness for Hele-Shaw-type free boundary problems with sign-changing velocity are proved in general dimension.

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