{"paper":{"title":"Strong solution for stochastic transport equations with irregular drift: existence and non-existence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangying Lv, Hongjun Gao, Jinlong Wei, Jinqiao Duan","submitted_at":"2017-11-14T12:10:07Z","abstract_excerpt":"We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a $q$-integrable (in time), bounded and $\\alpha$-H\\\"{o}lder continuous (in space) drift coefficient. More precisely, we show that for a Sobolev differentiable initial condition, there exists a unique stochastic strong solution when $\\alpha>2/q$, while for $\\alpha+1<2/q$ with spatial dimension higher than one, we can choose proper initial data and drift coefficients so that there is no stochastic strong solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05072","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"}