{"paper":{"title":"Invariant measures for Burgers equation with stochastic forcing","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. E. Mazel, K. M. Khanin, Weinan E, Ya. G. Sinai","submitted_at":"2000-05-01T00:00:00Z","abstract_excerpt":"In this paper we study the following Burgers equation\n  du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t)\n  where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t.  We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts all other solutions with the same forcing. This is done by studying the so-called one-sided minimiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0005306","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"}