{"paper":{"title":"The A-Stokes approximation for non-stationary problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominic Breit","submitted_at":"2014-02-13T08:51:03Z","abstract_excerpt":"Let $\\mathcal A$ be an elliptic tensor. A function $v\\in L^1(I;LD_{div}(B))$ is a solution to the non-stationary $\\mathcal A $-Stokes problem iff \\begin{align}\\label{abs} \\int_Q v\\cdot\\partial_t\\phi\\,dx\\,dt-\\int_Q \\mathcal A(\\varepsilon(v),\\varepsilon(\\phi))\\,dx\\,dt=0\\quad\\forall\\phi\\in C^{\\infty}_{0,div}(Q), \\end{align} where $Q:=I\\times B$, $B\\subset\\mathbb R^d$ bounded. If the l.h.s. is not zero but small we talk about almost solutions. We present an approximation result in the fashion of the $\\mathcal A$-caloric approximation for the non-stationary $\\mathcal A $-Stokes problem. Precisely, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3064","kind":"arxiv","version":3},"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"}