{"paper":{"title":"Global entropy solutions to the compressible Euler equations in the isentropic nozzle flow for large data: Application of the modified Godunov scheme and the generalized invariant regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Naoki Tsuge","submitted_at":"2017-02-10T21:58:06Z","abstract_excerpt":"We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These phenomena are governed by the compressible Euler equation, which is one of crucial equations in inhomogeneous conservation laws.\n  In this paper, we consider its unsteady flow and devote to proving the global existence and stability of solutions to the Cauchy problem for the general nozzle. The theorem has been proved in (Tsuge in Arch. Ration. Mech. Anal. 209:36"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03333","kind":"arxiv","version":2},"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"}