{"paper":{"title":"Almost optimal local well-posedness for the Maxwell-Klein-Gordon system with data in Fourier-Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hartmut Pecher","submitted_at":"2019-08-15T17:48:04Z","abstract_excerpt":"We prove a low regularity local well-posedness result for the Maxwell-Klein-Gordon system in three space dimensions for data in Fourier - Lebesgue spaces $\\widehat{H}^{s,r}$ , where $\\|f\\|_{\\widehat{H}^{s,r}} = \\|\\langle \\xi \\rangle^s \\widehat{f}(\\xi)\\|_{\\widehat{L}^{r'}}$ , $\\frac{1}{r}+\\frac{1}{r'} = 1$ . The assumed regularity for the data is almost optimal with respect to scaling as $r \\to 1$ . This closes the gap between what is known in the case $r=2$ , namely $s > \\frac{3}{4}$ , and the critical value $s_c = \\frac{1}{2}$ with respect to scaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05651","kind":"arxiv","version":3},"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/1908.05651/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"}