{"paper":{"title":"Propagation of chaos for some 2 dimensional fractional Keller Segel equations in diffusion dominated and fair competition cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Samir Salem","submitted_at":"2017-12-18T21:15:44Z","abstract_excerpt":"In this work we deal with the local in time propagation of chaos without cut-off for some two dimensional fractional Keller Segel equations. More precisely the diffusion considered here is given by the fractional Laplacian operator $-(-\\Delta)^{\\frac{a}{2}}$ with $a \\in (1,2)$ and the singularity of the interaction is of order $|x|^{1-\\alpha}$ with $\\alpha\\in ]1,a]$. In the case $\\alpha\\in (1,a)$ we give a complete propagation of chaos result, proving the $\\Gamma$-l.s.c property of the fractional Fisher information, already known for the classical Fisher information, using a result of Mischler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06677","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"}