{"paper":{"title":"Nondispersive solutions to the mass critical half-wave equation in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vladimir Georgiev, Yuan Li","submitted_at":"2020-07-30T10:46:07Z","abstract_excerpt":"We consider the half-wave equation with mass critical in two dimension \\begin{eqnarray*} \\begin{cases} iu_t=Du-|u|u,\\,\\,\\, \\\\ u(0,x)=u_0(x), \\end{cases} \\end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass $\\|u_0\\|_2=\\|Q\\|_2$, where $Q$ is the ground state solution of equation $DQ+Q=Q^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.15370","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.15370/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"}