{"paper":{"title":"Remarks on Oldroyd-B and Related Complex Fluids Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter Constantin, Weiran Sun","submitted_at":"2010-09-01T19:14:59Z","abstract_excerpt":"We prove global existence and uniqueness of solutions of Oldroyd-B systems with relatively small data in $\\Rr^d$, in a large functional setting ($C^{\\alpha}\\cap L^1$). This is a stability result, solutions select an equilibrium and converge exponentially to it. Large spatial derivatives of the initial density and stress are allowed, provided the $L^{\\infty}$ norm of the density and stress are small enough. We prove global regularity for large data for a model in which the potential responds to high rates of strain in the fluid. We also prove global existence for a class of large data for a did"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0249","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"}