{"paper":{"title":"On the local and global existence of solutions to 1D transport equations with nonlocal velocity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hantaek Bae, Omar Lazar, Rafael Granero-Belinch\\'on","submitted_at":"2018-06-04T08:46:18Z","abstract_excerpt":"We consider the 1D transport equation with nonlocal velocity field: \\begin{equation*}\\label{intro eq} \\begin{split} &\\theta_t+u\\theta_x+\\nu \\Lambda^{\\gamma}\\theta=0, \\\\ & u=\\mathcal{N}(\\theta), \\end{split} \\end{equation*} where $\\mathcal{N}$ is a nonlocal operator. In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01011","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"}