{"paper":{"title":"Stable self-similar singularity formation for infinite energy solutions of the incompressible porous medium equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Charles Collot, Christophe Prange, Jin Tan","submitted_at":"2025-07-23T10:24:57Z","abstract_excerpt":"We consider a special class of infinite energy solutions to the inviscid incompressible porous medium equations (IPM), introduced in Castro-C\\'ordoba-Gancedo-Orive [9]. The (IPM) equations then reduce to a one-dimensional nonlocal nonlinear equation, for which an explicit self-similar blow-up solution is found in [9]. We show the stability of this explicit blow-up solution by smooth enough perturbations, and identity a sharp regularity threshold below which it is unstable. The heart of our proof is a change of variables that transforms the study of finite time blow-up solutions, to the study o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17381","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.17381/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}