{"paper":{"title":"Local existence of solutions and blow-up criteria for the Boussinesq equations in Lei-Lin-Gevrey Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Patr\\'icia L. Guidolin, Thyago S.R. Santos, Wilberclay G. Melo","submitted_at":"2026-05-29T15:52:01Z","abstract_excerpt":"This paper studies the local well-posedness and the behavior at potential finite blow-up times of mild solutions to the three-dimensional fractional Boussinesq equations in Lei-Lin and Lei-Lin-Gevrey spaces $\\mathcal{X}_{a,\\sigma}^s(\\mathbb{R}^3)$. By combining fixed point arguments with Fourier estimates adapted to these spaces, we obtain local existence and uniqueness results for data in $\\mathcal{X}_{a,\\sigma}^s(\\mathbb{R}^3)$, including the usual Lei-Lin case $a=0$. We also establish several blow-up criteria for maximal mild solutions and derive lower bounds for the growth of the correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31461","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/2605.31461/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"}