{"paper":{"title":"Global regularity for 2D Boussinesq temperature patches with no diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eduardo Garcia-Juarez, Francisco Gancedo","submitted_at":"2016-11-30T16:45:38Z","abstract_excerpt":"This paper considers the temperature patch problem for the incompressible Boussinesq system with no diffusion and viscosity in the whole space $\\mathbb{R}^2$. We prove that for initial patches with $W^{2,\\infty}$ boundary the curvature remains bounded for all time. The proof explores new cancellations that allow us to bound $\\nabla^2u$, even for those components given by time dependent singular integrals with kernels with nonzero mean on circles. In addition, we give a different proof of the $C^{1+\\gamma}$ regularity result in [23], $0<\\gamma<1$, using the scale of Sobolev spaces for the veloc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10260","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":""},"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"}