{"paper":{"title":"The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space","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, Vedran Sohinger","submitted_at":"2012-05-31T20:36:38Z","abstract_excerpt":"We prove that $k$-th order derivatives of perturbative classical solutions to the hard and soft potential Boltzmann equation (without the angular cut-off assumption) in the whole space, ${\\mathbb R}^{n}_x$ with $n \\ge 3$, converge in large-time to the global Maxwellian with the optimal decay rate of $O(t^{-1/2(k+\\varrho+\\frac{n}{2}-\\frac{n}{r})})$ in the $L^r_x(L^2_{v})$-norm for any $2\\leq r\\leq \\infty$. These results hold for any $\\varrho \\in [0, n/2]$ as long as initially $\\| f_0|_{\\dot{B}^{-\\varrho,\\infty}_2 L^2_{v}} < \\infty$. In the hard potential case, we prove faster decay results in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0027","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"}