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For the first result, we obtain the estimate of weak solutions in $L^{\\alpha}_{t}L_{v}^{3-\\eps}$ for $\\alpha=\\frac{2(3-\\eps)}{3(2-\\eps)}$ and $0<\\eps<1$, which is an improvement over estimates by Fournier-Guerin [N. Fournier; H. Guerin, Well-posedness of the spatially homogeneous Landau equation for soft potentials. J. Funct. Anal. 25(2009), no. 8, 2542--2560]. Foe the second result, we have the estimate of weak solutions in $L_{t}^{\\infty}L^{p}_{v}$, $p"},"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":"1306.1220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-05T19:51:58Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2e3983fbc0ac55ff696c99cf9024f6db62bf15b6da98b883f59d0e5bb6847937","abstract_canon_sha256":"5f7e3f19d302af90d12ae3fd8f881ec47ecade865e42f10cc420436949a4b667"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:58.721276Z","signature_b64":"Ic0uwIdgL+XKuCNlAFUGaDQPsQLqnnZ3NsPb3/X1QK4Jg1NC8iDcYlfAfFfo+AcDsIJ9AOcm3JjS7RWTt+niBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f319068b9a2403f6ecde38903d570fe5c61eaae6ff67f230e26471db48238626","last_reissued_at":"2026-05-18T03:19:58.720803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:58.720803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global in Time Estimates for the Spatially Homogeneous Landau Equation with Soft Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kung-Chien Wu","submitted_at":"2013-06-05T19:51:58Z","abstract_excerpt":"This paper deals with some global in time a priori estimates of the spatially homogeneous Landau equation for soft potentials $\\ga\\in[-2,0)$. 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