{"paper":{"title":"TVD Fields and Isentropic Gas Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Geng Chen, Helge Kristian Jenssen","submitted_at":"2012-02-01T04:19:54Z","abstract_excerpt":"Little is known about global existence of large-variation solutions to Cauchy problems for systems of conservation laws in one space dimension. Besides results for $L^\\infty$ data via compensated compactness, the existence of global BV solutions for arbitrary BV data remains an outstanding open problem. In particular, it is not known if isentropic gas dynamics admits an a priori variation bound which applies to all BV data.\n  In a few cases such results are available: scalar equations, Temple class systems, $2\\times 2$-systems satisfying Bakhvalov's condition, and, in particular, isothermal ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0093","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"}