{"paper":{"title":"On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Argenis Mendez","submitted_at":"2019-02-21T22:59:10Z","abstract_excerpt":"We consider the initial value problem (IVP) for the fractional Korteweg-de Vries equation (fKdV) \\begin{equation}\\label{abstracteq1} \\left\\{ \\begin{array}{ll} \\partial_{t}u-D_{x}^{\\alpha}\\partial_{x}u+u\\partial_{x}u=0, & x,t\\in\\mathbb{R},\\,0<\\alpha<1, \\\\ u(x,0)=u_{0}(x).& \\\\ \\end{array} \\right. \\end{equation} It has been shown that the solutions to certain dispersive equations satisfy the propagation of regularity phenomena. More precisely, it deals in determine whether regularity of the initial data on the right hand side of the real line is propagated to the left hand side by the flow soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08296","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"}