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For $\\alpha > 1 $ and close to $1$, we establish finite time nearly self-similar blowup from some smooth initial data $f_0 \\geq 0$, which can be both radially symmetric or non-radially symmetric. The blowup results are sharp as the homogeneous Landau equation $(\\alpha=1)$ is globally well-pose"},"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":"2311.11511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-20T03:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"5f17acba5986e11c678147f4b7bb0c67d33e1ccc633ae1149b3ffcf96b92407f","abstract_canon_sha256":"b2e32c7989d3bfd28bfccd818b8ce80304f3ea5f96039a994ceb7a1be79d045c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:14:34.382075Z","signature_b64":"ieNL/KSogw47Xt7A6uqdgnZ1AWyziJxyXRfubSa24Os5F51cvjwfonpfgd9CX4qxIKRZu9pebNgTXcuH/MHoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a6323a086914e37bd8ca6534c5073a643bf978f12a3579320e09923fba0976","last_reissued_at":"2026-07-05T07:14:34.381613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:14:34.381613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nearly self-similar blowup of the slightly perturbed homogeneous Landau equation with very soft potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiajie Chen","submitted_at":"2023-11-20T03:20:14Z","abstract_excerpt":"We study the slightly perturbed homogeneous Landau equation \\[ \\partial_t f = a_{ij}(f) \\cdot \\partial_{ij} f + \\alpha c(f) f, \\quad c(f) = - \\partial_{ij} a_{ij}(f), \\] with very soft potentials, where we increase the nonlinearity from $ c(f) f$ in the Landau equation to $\\alpha c(f) f$ with $\\alpha>1$. For $\\alpha > 1 $ and close to $1$, we establish finite time nearly self-similar blowup from some smooth initial data $f_0 \\geq 0$, which can be both radially symmetric or non-radially symmetric. 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