{"paper":{"title":"Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hirokazu Saito, Matthias Hieber","submitted_at":"2015-09-11T09:08:17Z","abstract_excerpt":"Consider the two-phase free boundary problem subject to surface tension and gravitational forces for a class of non-Newtonian fluids with stress tensors $T_i$ of the form $T_i=-\\pi I+\\mu_i(|D(v)|^2)D(v)$ for $i=1,2$, respectively, and where the viscosity functions $\\mu_i$ satisfy $\\mu_i(s)\\in C^3([0,\\infty))$ and $\\mu_i(0)>0$ for $i=1,2$. It is shown that for given $T>0$ this problem admits a unique, strong solution on $(0,T)$ provided the initial data are sufficiently small in their natural norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03428","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"}