{"paper":{"title":"The \"good\" Boussinesq equation on the half-line with Robin boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The good Boussinesq equation on the half-line is locally well-posed in the Hadamard sense with nonzero Robin boundary conditions.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dionyssios Mantzavinos, Shivani Agarwal","submitted_at":"2026-05-14T03:59:40Z","abstract_excerpt":"We prove the local Hadamard well-posedness of the ``good'' Boussinesq equation formulated on the half-line with nonzero Robin boundary conditions. These boundary data involve the Dirichlet and Neumann boundary values as well as the second spatial derivative of the solution evaluated at the boundary. The nonlinear analysis crucially relies on the linear estimates established through the explicit solution formula obtained for the forced linear counterpart of the problem via Fokas's unified transform. The two pieces of initial data and the two pieces of boundary data belong in appropriate Sobolev"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove the local Hadamard well-posedness of the ``good'' Boussinesq equation formulated on the half-line with nonzero Robin boundary conditions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The nonlinear analysis crucially relies on the linear estimates established through the explicit solution formula obtained for the forced linear counterpart of the problem via Fokas's unified transform.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Local Hadamard well-posedness is proved for the good Boussinesq equation on the half-line with nonzero Robin boundary conditions, with solutions in Sobolev spaces that depend continuously on initial and boundary data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The good Boussinesq equation on the half-line is locally well-posed in the Hadamard sense with nonzero Robin boundary conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"50360bde9e21308f70a2f6d95bdae3e2e8310ea6a60fb6bf95ebc4148e10c7d2"},"source":{"id":"2605.14335","kind":"arxiv","version":1},"verdict":{"id":"1d267481-96c2-4b6f-a289-2f2e789d3fa2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:25:25.748831Z","strongest_claim":"We prove the local Hadamard well-posedness of the ``good'' Boussinesq equation formulated on the half-line with nonzero Robin boundary conditions.","one_line_summary":"Local Hadamard well-posedness is proved for the good Boussinesq equation on the half-line with nonzero Robin boundary conditions, with solutions in Sobolev spaces that depend continuously on initial and boundary data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The nonlinear analysis crucially relies on the linear estimates established through the explicit solution formula obtained for the forced linear counterpart of the problem via Fokas's unified transform.","pith_extraction_headline":"The good Boussinesq equation on the half-line is locally well-posed in the Hadamard sense with nonzero Robin boundary conditions."},"references":{"count":13,"sample":[{"doi":"","year":2024,"title":"[AM ¨O24] A. Alkin, D. Mantzavinos, and T. ¨Ozsarı,Local well-posedness of the higher-order nonlinear Schr¨ odinger equation on the half-line: Single-boundary condition case, Studies in Applied Mathem","work_id":"53c74538-9f41-4aa4-b949-c0645b5d5f60","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1988,"title":"Dynamical Systems and Complexity","work_id":"d7629476-7dd7-46bd-aafa-f7c5fa0c05ba","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Cavalcante,The initial boundary value problem for some quadratic nonlinear Schr¨ odinger equations on the half-line, Differential Integral Equations30(2017), no","work_id":"4cf62011-2c97-458b-b0a5-c65389183097","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"[Fam24] A. V. Faminskii,Global weak solutions of an initial-boundary value problem on a half-line for the higher order nonlinear Schr¨ odinger equation, J. Math. Anal. Appl.533(2024), no. 2, Paper No.","work_id":"6bb2b0e8-1473-49de-9a01-b4589445a3ef","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"[Far09] L. G. Farah,Local solutions in Sobolev spaces with negative indices for the “good” Boussinesq equation, Comm. Partial Differential Equations34(2009), no. 1-3, 52–73. [FHM16] A. S. Fokas, A. A.","work_id":"bffd9861-eb37-430c-acf7-afb21eddaa51","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"1100d9e30f7785c25d3f07308cb7b3e0c636db1b7eb1d2bd4e66754cdbe20ab4","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"}