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Finite time singularities of smooth solutions for the 2D incompressible porous media (IPM) equation with a smooth source

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arxiv 2410.22920 v3 pith:ZWX7R47E submitted 2024-10-30 math.AP

Diego Córdoba , Luis Martínez-Zoroa This is my paper · ORCID
classification math.AP
keywords smoothequationfiniteincompressiblemediaporoussingularitiessolutions
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We establish the existence of smooth, finite-energy solutions to the 2D incompressible porous media equation (IPM), with a compactly supported uniformly smooth source, which develop singularities in finite time.

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  1. Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\epsilon}\cap L^2$ force

    math.AP 2025-05 conditional novelty 7.0 of 10

    There exist compactly supported, smooth-before-blow-up solutions of the forced 2D Boussinesq equation that blow up in finite time with a uniformly C^{1,alpha} cap L^2 force for every alpha < sqrt(4/3)-1.

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