{"paper":{"title":"Suppression of blow-up in Parabolic-Parabolic Patlak-Keller-Segel via strictly monotone shear flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Siming He","submitted_at":"2017-10-27T19:46:23Z","abstract_excerpt":"In this paper we consider the parabolic-parabolic Patlak-Keller-Segel models in $\\mathbb{T}\\times\\mathbb{R}$ with advection by a large strictly monotone shear flow. Without the shear flow, the model is $L^1$ critical in two dimensions with critical mass $8\\pi$: solutions with mass less than $8\\pi$ are global in time and there exist solutions with mass larger than $8 \\pi$ which blow up in finite time \\cite{Schweyer14}. We show that the additional shear flow, if it is chosen sufficiently large, suppresses one dimension of the dynamics and hence can suppress blow-up. In contrast with the paraboli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10315","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"}