{"paper":{"title":"Multiphase formulation of the Vlasov-Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Valentin Lemarie (LAMA)","submitted_at":"2026-06-29T09:25:17Z","abstract_excerpt":"In this paper, we study a particular family of solutions of the Vlasov-Navier-Stokes system posed on $\\mathbb{R}^d$ (with $d\\geq 2$), and show their convergence to the unique solution of the pressureless Euler-Navier-Stokes system. A global existence result for the latter system, in the small data regime, was established in \\cite{MonENS}. Here we place ourselves in a multiphase framework, introduced and studied by Zakharov in \\cite{Zakharov1,Zakharov2}, in order to carry out an analogous analysis for a system that we will call multiphase pressureless Euler-Navier-Stokes. We then study the sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30022","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/2606.30022/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"}