{"paper":{"title":"Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dingqun Deng, Shota Sakamoto","submitted_at":"2026-02-17T14:12:51Z","abstract_excerpt":"We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=\\mu+\\mu^{\\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the norm $\\|f\\|_{L^\\infty_t L^{r}_{x,v}}+\\|f\\|_{L^\\infty_t L^2_{x,v}}$ remains bounded for some sufficiently large $r>0$. As a byproduct, we establish $L^2_{t,x,v}$ stability for initial data $f_0\\in L^r_{x,v}\\cap L^2_{x,v}$. Our approach employs dilated dyadic decompositions in phase space $(v,\\xi,\\eta)$ to capture hypoellipticity and to reduce the fractional de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.15601","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.15601/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}