{"paper":{"title":"Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Akansha Sanwal, Shinya Kinoshita, Shohei Nakamura","submitted_at":"2022-12-04T12:09:55Z","abstract_excerpt":"In this paper, we establish local well-posedness for the Zakharov system on $\\mathbb{T}^d$, $d\\ge3$ in a low regularity setting. Our result improves the work of Kishimoto. Moreover, the result is sharp up to $\\varepsilon$-loss of regularity when $d=3$ and $d\\ge5$ as long as one utilizes the iteration argument. We introduce ideas from recent developments of the Fourier restriction theory. The key element in the proof of our well-posedness result is a new trilinear discrete Fourier restriction estimate involving paraboloid and cone. We prove this trilinear estimate by improving Bourgain--Demeter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01805","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.01805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}