{"paper":{"title":"Parabolic equations with singular divergence-free drift vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangyu Xi, Zhongmin Qian","submitted_at":"2016-12-22T17:54:30Z","abstract_excerpt":"In this paper, we study an elliptic operator in divergence-form but not necessary symmetric. In particular, our results can be applied to elliptic operator $L=\\nu\\Delta+u(x,t)\\cdot\\nabla$, where $u(\\cdot,t)$ is a time-dependent vector field in $\\mathbb{R}^{n}$, which is divergence-free in distribution sense, i.e. $\\nabla\\cdot u=0$. Suppose $u\\in L_{t}^{\\infty}(\\textrm{BMO}_{x}^{-1})$. We show the existence of the fundamental solution $\\varGamma(x,t;\\xi,\\tau)$ of the parabolic operator $L-\\partial_{t}$, and show that $\\varGamma$ satisfies the Aronson estimate with a constant depending only on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07727","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"}