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t\\in\\mathbb R,\\\\ u(x,0)&\\hspace{-2mm}=u_0(x). \\end{array} \\right\\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$Z_{s,\\frac{s}2}:=\\{u\\in H^s(\\mathbb R):D_x^{-s} u\\in L^2(\\mathbb R)\\}\\cap L^2(|x|^s dx ),$$ with $\\frac34<s\\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00783","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":"1603.00783","created_at":"2026-05-18T01:19:42.977857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00783v1","created_at":"2026-05-18T01:19:42.977857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00783","created_at":"2026-05-18T01:19:42.977857+00:00"},{"alias_kind":"pith_short_12","alias_value":"5XRI3NW77FJC","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5XRI3NW77FJCX5GH","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5XRI3NW7","created_at":"2026-05-18T12:30:01.593930+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/5XRI3NW77FJCX5GHVFMEIQTDBE","json":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE.json","graph_json":"https://pith.science/api/pith-number/5XRI3NW77FJCX5GHVFMEIQTDBE/graph.json","events_json":"https://pith.science/api/pith-number/5XRI3NW77FJCX5GHVFMEIQTDBE/events.json","paper":"https://pith.science/paper/5XRI3NW7"},"agent_actions":{"view_html":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE","download_json":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE.json","view_paper":"https://pith.science/paper/5XRI3NW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00783&json=true","fetch_graph":"https://pith.science/api/pith-number/5XRI3NW77FJCX5GHVFMEIQTDBE/graph.json","fetch_events":"https://pith.science/api/pith-number/5XRI3NW77FJCX5GHVFMEIQTDBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE/action/storage_attestation","attest_author":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE/action/author_attestation","sign_citation":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE/action/citation_signature","submit_replication":"https://pith.science/pith/5XRI3NW77FJCX5GHVFMEIQTDBE/action/replication_record"}},"created_at":"2026-05-18T01:19:42.977857+00:00","updated_at":"2026-05-18T01:19:42.977857+00:00"}