{"paper":{"title":"The regularized 3D Boussinesq equations with fractional Laplacian and no diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benedetta Ferrario, Hakima Bessaih","submitted_at":"2015-04-20T14:15:21Z","abstract_excerpt":"In this paper, we study the 3D regularized Boussinesq equations. The velocity equation is regularized \\`a la Leray through a smoothing kernel of order $\\alpha$ in the nonlinear term and a $\\beta$-fractional Laplacian; we consider the critical case $\\alpha+\\beta=\\frac{5}{4}$ and we assume $\\frac 12 <\\beta<\\frac 54$. The temperature equation is a pure transport equation, where the transport velocity is regularized through the same smoothing kernel of order $\\alpha$. We prove global well posedness when the initial velocity is in $H^r$ and the initial temperature is in $H^{r-\\beta}$ for $r>\\max(2\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05067","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}