{"paper":{"title":"Pointwise estimates for solutions of 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":"2015-08-03T10:54:00Z","abstract_excerpt":"In this paper, we provide two-sided estimates and uniform asymptotics for the solution of $d$-dimensional critical fractal Burgers equation $u_t-\\Delta^{\\alpha/2}u+b\\cdot \\nabla\\left(u|u|^q\\right)=0$, $\\alpha\\in(1,2)$, $b\\in\\mathbb R^d$ for $q = (\\alpha-1)/d$ and $u_0 \\in L^1(\\mathbb R^d)$. We consider also $q > (\\alpha-1)/d$ under additional condition $u_0 \\in L^\\infty(\\mathbb R^d)$. In both cases we assume $u_0\\geq0$, which implies that the solution is non-negative. The estimates are given in the terms of the function $P_t u_0$, where $P_t$ is the stable semigroup operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00370","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"}