{"paper":{"title":"Variational Inequalities of Navier--Stokes Type with Time Dependent Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marek Niezg\\'odka, Maria Gokieli, Nobuyuki Kenmochi","submitted_at":"2016-12-21T13:30:52Z","abstract_excerpt":"We consider a class of parabolic variational inequalities with time dependent obstacle of the form $|{\\boldsymbol u}(x,t)| \\le p(x,t)$, where ${\\boldsymbol u}$ is the velocity field of a fluid governed by the Navier--Stokes variational inequality. The obstacle function $p=p(x,t)$ imposed on ${\\boldsymbol u}$ consists of three parts which are respectively the degenerate part $p(x,t)=0$, the finitely positive part $0< p(x,t) <\\infty$ and singular part $p(x,t)=\\infty$. In this paper, we shall propose a sequence of approximate obstacle problems with everywhere finitely positive obstacles and prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07099","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"}