{"paper":{"title":"Strong and Weak Solutions to the Hasegawa-Mima Equation with Periodic Boundary Conditions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Hagop Karakazian, Nabil Nassif","submitted_at":"2017-12-15T04:20:31Z","abstract_excerpt":"The two dimensional Hasegawa-Mima (HM) equation $$ -\\Delta u_t+u_t = \\{u,\\Delta u\\} + ku_y$$ describes the time evolution of drift waves in magnetically-confined plasma. Several authors have treated the HM equation theoretically and numerically, with difficulties arising when handling the non-linear Poisson's bracket $\\{u,\\Delta u\\}:=u_x\\Delta u_u-u_y\\Delta u_x $. In this paper, we introduce a new decoupling approach that avoids the Poisson's bracket term by reformulating the HM equation as a system of two linear PDEs, a solution of which is a pair $(u,w)$ such that $$(HM)\\,\\,\\,\\left\\{\\begin{a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05524","kind":"arxiv","version":5},"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/1712.05524/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"}