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arXiv · 2511.01827

Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass

Kevin H. Dembski
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Abstract

We prove finite-time singularity formation for Lipschitz continuous solutions of the inviscid porous medium equation which vanish on the boundary of the domain. As the density vanishes on the boundary of the domain, the full regularizing effect of transport is present and must be overcome. The solutions are smooth away from the origin and the density can be made compactly supported.

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Kevin H. Dembski. 2025-11-03. Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass. https://arxiv.org/abs/2511.01827

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