{"paper":{"title":"Well-posedness and blow-up criterion for strong solutions of the compressible Navier-Stokes/Allen-Cahn system with vacuum","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haoran Zheng, Junquan Zhou, Yinghua Li","submitted_at":"2026-05-23T13:02:40Z","abstract_excerpt":"This paper is devoted to the study of strong solutions for the compressible Navier-Stokes/Allen-Cahn system in bounded domain $\\Omega\\subset\\mathbb R^3$, allowing for the presence of initial vacuum. A characteristic of this system is the strong coupling between density and the Allen-Cahn equation, which leads to strong degeneracy in vacuum regions. Under a compatibility condition on the initial phase-field variable, we establish the local existence and uniqueness of strong solutions for $0\\le\\rho_0\\in W^{1,q}$ with $q\\in(3,6)$, $u_0\\in H_0^1$ and $\\chi_0\\in H^2$. Owing to time-weighted estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24568","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}