{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R","short_pith_number":"pith:2NPLSJJE","schema_version":"1.0","canonical_sha256":"d35eb92524d1c26b1f3bcd13d38989f450035de4cb08566968f7cb1609b43bb3","source":{"kind":"arxiv","id":"1711.05067","version":1},"attestation_state":"computed","paper":{"title":"Existence and uniqueness of $W^{1,r}_{loc}$-solutions for stochastic transport equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangying Lv, Hongjun Gao, Jinlong Wei, Jinqiao Duan","submitted_at":"2017-11-14T12:00:40Z","abstract_excerpt":"We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\\mathbb R}^d;{\\mathbb R}^d))$ drift coefficient and $W^{1,r}({\\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of stochastic strong solutions (in $W^{1,r}_{loc}({\\mathbb R}^d))$.In particular, when $r=\\infty$, we establish a Lipschitz estimate for solutions and this question is opened by Fedrizzi and Flandoli in case of $L^q(0,T;L^p({\\mathbb R}^d;{\\mathbb R}^d))$ drift coefficient. Moreover, opposite to the deterministic case where $L^q(0,T;W^{1,p}({\\mathbb R}^d;{\\mathbb R}"},"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":"1711.05067","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-14T12:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"54d7d64fcbd8e9564cf98fa1ab678e7c734911e0c32d897482c0bd46eef874d8","abstract_canon_sha256":"11be91b160b7ae97870720db8824f63609c86653c5048d75628fee0a8e580cc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:34.851681Z","signature_b64":"W8r1MzQR2GpKuKPRAeLqxXUDh1nvaBRoEwDcLao7CbHPkR82yytSvF/88WBrygoJkgLU0wuWUJRt+eWRsPg/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d35eb92524d1c26b1f3bcd13d38989f450035de4cb08566968f7cb1609b43bb3","last_reissued_at":"2026-05-18T00:30:34.850967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:34.850967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and uniqueness of $W^{1,r}_{loc}$-solutions for stochastic transport equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangying Lv, Hongjun Gao, Jinlong Wei, Jinqiao Duan","submitted_at":"2017-11-14T12:00:40Z","abstract_excerpt":"We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\\mathbb R}^d;{\\mathbb R}^d))$ drift coefficient and $W^{1,r}({\\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of stochastic strong solutions (in $W^{1,r}_{loc}({\\mathbb R}^d))$.In particular, when $r=\\infty$, we establish a Lipschitz estimate for solutions and this question is opened by Fedrizzi and Flandoli in case of $L^q(0,T;L^p({\\mathbb R}^d;{\\mathbb R}^d))$ drift coefficient. Moreover, opposite to the deterministic case where $L^q(0,T;W^{1,p}({\\mathbb R}^d;{\\mathbb R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05067","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.05067","created_at":"2026-05-18T00:30:34.851076+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05067v1","created_at":"2026-05-18T00:30:34.851076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05067","created_at":"2026-05-18T00:30:34.851076+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NPLSJJE2HBG","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NPLSJJE2HBGWHZ3","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NPLSJJE","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R","json":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R.json","graph_json":"https://pith.science/api/pith-number/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/graph.json","events_json":"https://pith.science/api/pith-number/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/events.json","paper":"https://pith.science/paper/2NPLSJJE"},"agent_actions":{"view_html":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R","download_json":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R.json","view_paper":"https://pith.science/paper/2NPLSJJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05067&json=true","fetch_graph":"https://pith.science/api/pith-number/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/graph.json","fetch_events":"https://pith.science/api/pith-number/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/action/storage_attestation","attest_author":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/action/author_attestation","sign_citation":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/action/citation_signature","submit_replication":"https://pith.science/pith/2NPLSJJE2HBGWHZ3ZUJ5HCMJ6R/action/replication_record"}},"created_at":"2026-05-18T00:30:34.851076+00:00","updated_at":"2026-05-18T00:30:34.851076+00:00"}