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In the model case $\\Psi(r)=r^s$, this equation couples nonlinear fast-diffusion/porous-medium type diffusion with kinetic transport. A distinctive feature is that the diffusion acts only in the velocity variable $v$, so that compactness in the spatial variable $x$ cannot be obtained from standard elliptic estimates and must instead be recovered through the hypoelliptic structure.\n  Under general struc"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.00458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T05:25:29Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9ef9ca2b6452232c149858c52ee29d6bd905cbd614b25a6cd9dcd83f18b57d3a","abstract_canon_sha256":"d9e38a96efc431c2c6c862e9d80b02499fb542987ed5df54815edbb1a4016f6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:44.021726Z","signature_b64":"WsbOD7X5c5bQfhyPwBb2SlfLJE0NXGwcqLwlWWkxelkSVekSYnyZef6gxFQCb/G5lRWIt4qJ0bc+2EItjhEqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acdf4d475dfececd67d1794fb31311ebcc0b2316dd5afe3dda5d43b014dce4d1","last_reissued_at":"2026-07-02T01:17:44.021303Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:44.021303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kinetic Fokker-Planck Equations with Nonlinear Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Xicheng Zhang, Zhengyan Wu, Zimo Hao","submitted_at":"2026-07-01T05:25:29Z","abstract_excerpt":"We study existence, regularity, and uniqueness for the nonlinear kinetic Fokker--Planck equation $$\n  \\partial_t f=\\Delta_v\\Psi(f)-v\\cdot\\nabla_x f,\n  \\qquad f|_{t=0}=f_0, $$ on $\\mathbb R^{2d}$. 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