{"paper":{"title":"Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eduard Feireisl, Hana Mizerova, Maria Lukacova-Medvidova","submitted_at":"2018-03-22T15:17:47Z","abstract_excerpt":"The Cauchy problem for the complete Euler system is in general ill posed in the class of admissible (entropy producing) weak solutions. This suggests there might be sequences of approximate solutions that develop fine scale oscillations. Accordingly, the concept of measure--valued solution that capture possible oscillations is more suitable for analysis. We study the convergence of a class of entropy stable finite volume schemes for the barotropic and complete compressible Euler equations in the multidimensional case. We establish suitable stability and consistency estimates and show that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08401","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"}