{"paper":{"title":"Stable estimates for source solution of critical fractal Burgers equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Grzegorz Serafin, Tomasz Jakubowski","submitted_at":"2015-07-28T09:32:21Z","abstract_excerpt":"In this paper, we provide two-sided estimates for the source solution of $d$-dimensional critical fractal Burgers equation $u_t-\\Delta^{\\alpha/2}+b\\cdot \\nabla\\left(u|u|^q\\right)=0$, $q=(\\alpha-1)/d$, $\\alpha\\in(1,2)$, $b\\in\\mathbb{R}^d$, by the density function of the isotropic $\\alpha$-stable process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07695","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"}