{"paper":{"title":"Norm Inflation for Inviscid and Fully Dissipative Boussinesq Systems in Supercritical Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qionglei Chen, Yaowei Xie","submitted_at":"2026-07-15T10:43:16Z","abstract_excerpt":"We prove norm inflation, in the sense of strong ill-posedness, for the two-dimensional Boussinesq system in supercritical Besov spaces. For the inviscid system, norm inflation holds in \\(\\dot B^\\beta_{p,q}(\\mathbb R^2)\\times \\dot B^\\beta_{p,r}(\\mathbb R^2)\\) for \\(\\beta\\neq0\\), \\(1<p\\leq\\infty\\), \\(1\\leq q,r\\leq\\infty\\), and \\(-2<\\beta-\\frac{2}{p}<1\\). For the fully dissipative system, the same conclusion holds in the range \\(-2<\\beta-\\frac{2}{p}<-1\\). In both cases, the results cover almost all supercritical Besov spaces satisfying the local integrability condition. Norm inflation occurs in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13694","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/2607.13694/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"}