{"paper":{"title":"Large time blow up for a perturbation of the cubic Szeg\\H{o} equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haiyan Xu (LM-Orsay)","submitted_at":"2013-07-19T17:23:26Z","abstract_excerpt":"We consider the following Hamiltonian equation on a special manifold of rational functions, \\[i\\p\\_tu=\\Pi(|u|^2u)+\\al (u|1),\\ \\al\\in\\R,\\] where $\\Pi $ denotes the Szeg\\H{o} projector on the Hardy space of the circle $\\SS^1$. The equation with $\\al=0$ was first introduced by G{\\'e}rard and Grellier in \\cite{GG1} as a toy model for totally non dispersive evolution equations. We establish the following properties for this equation. For $\\al\\textless{}0$, any compact subset of initial data leads to a relatively compact subset of trajectories. For $\\al\\textgreater{}0$, there exist trajectories on w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5284","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":""},"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"}