{"paper":{"title":"Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Robert M. Strain","submitted_at":"2010-04-29T21:38:46Z","abstract_excerpt":"We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time \"mild\" solutions are obtained uniformly in the speed of light parameter $c \\ge 1$.  We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of  the Newtonian Boltzmann equation in the limit as $c\\to\\infty$ on arbitrary time intervals $[0,T]$, with  convergence rate $1/c^{2-\\epsilon}$ for any $\\epsilon \\in(0,2)$.  This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5407","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"}