{"paper":{"title":"The existence of the global entropy weak solutions for a generalized Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunxia Guan, Xi Tu, Zhaoyang Yin","submitted_at":"2017-03-13T01:37:54Z","abstract_excerpt":"In this paper, we prove the existence of a global entropy weak solution $u\\in H^1(\\mathbb{R})$ and $\\partial_{x}u\\in L^1(\\mathbb{R})\\cap BV(\\mathbb{R})$ for the Cauchy problem of a generalized Camassa-Holm equation by the viscous approximation method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04218","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":""},"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"}