{"paper":{"title":"Homogenization of an advection equation with locally stationary random coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tomasz Komorowski, Tymoteusz Chojecki","submitted_at":"2018-09-06T17:16:12Z","abstract_excerpt":"In the paper we consider the solution of an advection equation with rapidly changing coefficients $\\partial_t u_\\eps+(1/\\eps)V(t\\eps^{-2},x/{\\eps})\\cdot\\nabla_x u_\\eps=0$ for $t<T$ and $u_\\eps(T,x)=u_0(x)$, $x\\in\\bbR^d$. Here $\\eps>0$ is some small parameter and the drift term $\\left(V(t,x)\\right)_{(t,x)\\in \\bbR^{1+d}}$ is assumed to be a $d$-dimensional, vector valued random field with incompressible spatial realizations. We prove that when the field is Gaussian, locally stationary, quasi-periodic in the $x$ variable and strongly mixing in time the solutions $u_\\eps(t,x)$ converge in law, as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02099","kind":"arxiv","version":2},"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"}