{"paper":{"title":"Regularization by noise and stochastic Burgers equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"M. Gubinelli, M. Jara","submitted_at":"2012-08-31T16:57:45Z","abstract_excerpt":"We study a generalized 1d periodic SPDE of Burgers type: $$ \\partial_t u =- A^\\theta u + \\partial_x u^2 + A^{\\theta/2} \\xi $$ where $\\theta > 1/2$, $-A$ is the 1d Laplacian, $\\xi$ is a space-time white noise and the initial condition $u_0$ is taken to be (space) white noise. We introduce a notion of weak solution for this equation in the stationary setting. For these solutions we point out how the noise provide a regularizing effect allowing to prove existence and suitable estimates when $\\theta>1/2$. When $\\theta>5/4$ we obtain pathwise uniqueness. We discuss the use of the same method to stu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6551","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"}