{"paper":{"title":"A Two-Phase Free Boundary Problem for Axisymmetric Subsonic Euler Flows with Contact Discontinuities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Axisymmetric subsonic Euler flows with vorticity in infinite cylinders admit contact discontinuities.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyangdong Park","submitted_at":"2026-05-05T13:04:12Z","abstract_excerpt":"We study a free boundary problem for the three-dimensional steady compressible Euler equations in an infinitely long circular cylinder. The free boundary is a contact discontinuity separating two axisymmetric rotational subsonic flows, neither of which is prescribed a priori. The pressure continuity condition couples two unknown Euler states through an unknown interface, leading to a genuinely two-phase free boundary problem. Using a Helmholtz decomposition, we reformulate the pressure continuity condition as nonlinear boundary conditions for the Helmholtz variables. This reformulation reveals"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove the existence of contact discontinuities for axisymmetric subsonic Euler flows with non-zero vorticity and non-zero angular momentum density in three-dimensional infinitely long cylinders.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The cut-off domain problem can be solved via Helmholtz decomposition and iteration, and the limit as the domain becomes infinite preserves the contact discontinuity without introducing new singularities or violating subsonicity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence of contact discontinuities is proven for axisymmetric subsonic Euler flows with vorticity and angular momentum in 3D infinite cylinders via free boundary methods.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Axisymmetric subsonic Euler flows with vorticity in infinite cylinders admit contact discontinuities.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"047af720682aac6fa81db0546015afd2cd7ca847bc9bf7231197e78b98e3db2f"},"source":{"id":"2605.03714","kind":"arxiv","version":2},"verdict":{"id":"d26c6f28-2bc0-4206-a808-d2eaca6462b6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T14:58:39.045342Z","strongest_claim":"We prove the existence of contact discontinuities for axisymmetric subsonic Euler flows with non-zero vorticity and non-zero angular momentum density in three-dimensional infinitely long cylinders.","one_line_summary":"Existence of contact discontinuities is proven for axisymmetric subsonic Euler flows with vorticity and angular momentum in 3D infinite cylinders via free boundary methods.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The cut-off domain problem can be solved via Helmholtz decomposition and iteration, and the limit as the domain becomes infinite preserves the contact discontinuity without introducing new singularities or violating subsonicity.","pith_extraction_headline":"Axisymmetric subsonic Euler flows with vorticity in infinite cylinders admit contact discontinuities."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03714/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T13:35:59.668375Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:31:21.396103Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:05:08.894958Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1d990572eb2d32bfad34effff7fcc5a372b65d82e8ba30459562930fd6870e35"},"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"}