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By employing refined commutator estimates, the existence and uniqueness of global strong solutions are proved for small initial data $(Q_0,u_0)\\in H^{s+1}\\times H^s$ $(s\\geq 2)$ with activity $c>c_\\star$, which improves a previous result in \\cite{active-limit}. In addition, if the initial data further b","authors_text":"Fan Yang, Xiongfeng Yang","cross_cats":[],"headline":"Global strong solutions exist for the 3D active liquid crystal system when initial data are small and activity exceeds a critical threshold.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-06T08:13:36Z","title":"Global well-posedness and decay rates for the three dimensional incompressible active liquid crystals"},"references":{"count":69,"internal_anchors":1,"resolved_work":69,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"H. Abels, G. Dolzmann and Y . N. Liu,Well-posedness of a fully coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data, SIAM Journal on Mathematical Analysis, 2014, 46(4): 3050–3077","work_id":"5cad5379-a61b-4aff-aeb0-2c140f039844","year":2014},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"H. Abels, G. Dolzmann and Y . N. Liu,Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions, Advances in Differential Equations, 2016, ","work_id":"96390446-b1a5-4aab-8513-8aa58b4c05e0","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"De Anna,A global 2D well-posedness result on the order tensor liquid crystal theory, Journal of Differential Equations, 2017, 262(7): 3932–3979","work_id":"91bee664-b4af-4dfd-9771-817f655d6c46","year":2017},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"De Anna and A","work_id":"d8ddf72a-8f24-42fb-bd08-0ef9cf6b2aaa","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"J. M. Ball and A. Majumdar,Nematic liquid crystals: from Maier-Saupe to a continuum theory, Molecular crystals and liquid crystals, 2010, 525(1): 1–11","work_id":"7b8ac1d5-9bd3-4739-b02c-6d56cd9cd9d5","year":2010}],"snapshot_sha256":"b604bf880723c93b547820e848ad66e1237a798fe0e0811d5157a0abe1ab92fe"},"source":{"id":"2605.04625","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-19T17:51:43.849802Z","id":"125550d8-6c9c-4876-ab93-c8be90d42ff6","model_set":{"reader":"grok-4.3"},"one_line_summary":"Global well-posedness for small data and activity-dependent decay rates are established for the 3D Beris-Edwards active liquid crystal system using commutator estimates and Green's functions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Global strong solutions exist for the 3D active liquid crystal system when initial data are small and activity exceeds a critical threshold.","strongest_claim":"Existence and uniqueness of global strong solutions for small initial data (Q0,u0) in H^{s+1} x H^s (s>=2) when activity c > c_star, together with a mixing decay estimate on partial^k Q(t) that combines exponential decay at rate proportional to (c - c_star) Gamma and the optimal algebraic heat-kernel rate for k <= s-1.","weakest_assumption":"The initial data must be sufficiently small in the indicated Sobolev norms and the activity must exceed the critical threshold c_star; the proof relies on this smallness to close the a priori estimates via refined commutator bounds."}},"verdict_id":"125550d8-6c9c-4876-ab93-c8be90d42ff6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cfd10dd40a4229e800f0259a6d8af838d77ac16f8998a1d1a757d1eb3a38f35e","target":"record","created_at":"2026-05-20T00:00:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"201c5b4745aa4da60f4598251c52eaff87e56348682e61a525a8f1dda3bf3e2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-06T08:13:36Z","title_canon_sha256":"1b51ee3962d2b956cfd432dbafaeb77780bb0b357dda55845c89180cd93a8b5b"},"schema_version":"1.0","source":{"id":"2605.04625","kind":"arxiv","version":2}},"canonical_sha256":"79783b8975a36c82276239025dda1e0498613967dc18cd1b7adf25c9d366639d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79783b8975a36c82276239025dda1e0498613967dc18cd1b7adf25c9d366639d","first_computed_at":"2026-05-20T00:00:40.689362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:40.689362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2tF0upHbqMpdS4HuCmvRNO2YsfbULvI6q8Ktb/mkqFH/itpCL1kUDL8rTHhpcppQQLq0Sq1jMfmEPPxzJwSdDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:40.689986Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.04625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd10dd40a4229e800f0259a6d8af838d77ac16f8998a1d1a757d1eb3a38f35e","sha256:60c2a163a002bdfec0e9871446f34475abf5b077046721ff4a2ed88c9ab51c01"],"state_sha256":"06f42947864554e9bfaeaed3a929c06c69f2de35c3e880dbabe80362e96326e3"}