{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4b235fe48badcc62f1b75f8710b90e8262c997e64f3ae92ed2e884029ab125d4","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3329cf5117f4f5ecc687166087b77bc67c250f5641a81c2eaa2c4ef2621b3ba5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.kinetic-limits.landau-coulomb","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Charged particles in a plasma interact through many weak, long-range Coulomb nudges, described by the Landau collision equation. This equation has never been derived from Newton's laws.","posed_since":"1936","precise":"$N$ classical particles in $R^{3}$ with pair potential $\\epsilon^{(1/2)} \\phi(x/\\epsilon)$, $\\phi$ smooth and short-range, $N \\epsilon^{3} = 1$, $\\epsilon \\to 0$ (weak-coupling limit); the Coulomb case $e^{2}/\\mid x\\mid$ with a logarithmic cutoff is the harder variant. Prove that the one-particle marginal converges, for a positive time interval, to a solution of the Landau equation. Answer: a proof for a time interval of positive length.","problem_ref":null,"references":"","settled_by":"A rigorous propagation-of-chaos proof yielding the Landau equation for a positive time interval.","status_note":"Only formal derivations and partial results on truncated hierarchies exist (e.g. Bobylev, Pulvirenti and Saffirio, 2013).","title":"Derivation of the Landau equation for weakly coupled or Coulomb particles","topic_ref":"43f072b403d62b3c8ec7e10cd7a52d571053d785f7f84ce0ccb5bff0a60b87cc"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ec2ebf34d118e06f7466809ffa190c1401d99525b1852feb5cd9b60f9bd98b58","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c738604d9fbe0471db2128139d117688edb928af7c13d69347d22c6ad9a1556b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"3cgRnkOvrCB8KjiFNAnsAuLnaaPx4LuTYRw_zatojhUNAaU7bgfnHtP-wT5I1UnYwE2KeMe-goCIlx_WQnrzCg"},"schema":"pubphys.envelope/1"},"record_hash":"ec2ebf34d118e06f7466809ffa190c1401d99525b1852feb5cd9b60f9bd98b58","leaf_index":1638}