{
  "abstract": "We study the free-boundary Euler--Monge--Ampère system as a conservative relaxation of ideal incompressible fluid motion. The force is determined on the actual fluid domain by a Monge--Ampère equation coupled to a nonlinear boundary condition. For each fixed relaxation parameter, we establish local well-posedness for uniformly convex initial domains of class $C^{2,α}$, densities in $C^{1,α}$, and arbitrary initial velocities in $C^{2,α}$. The solution retains these spatial regularities, and the force potential belongs to $C^{3,α}$ up to the moving boundary. Within uniformly bounded data families, the solution depends continuously on the initial data at every lower Hölder exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16717",
  "author_total": 2,
  "authors": [
    {
      "name": "Sicheng Liu"
    },
    {
      "name": "Tao Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4m7x4vzcaajxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16717",
  "fulltext_url": null,
  "id": "4m7x4vzcaajxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16717",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7213403120",
  "pdf_url": "https://arxiv.org/pdf/2609.16717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4m7x4vzcaajxn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Local Well-posedness of Free Boundary Problems for the Euler--Monge--Ampère Equations",
  "title_text": "Local Well-posedness of Free Boundary Problems for the Euler--Monge--Ampère Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/4m7x4vzcaajxn",
  "venue": "arXiv",
  "versions": []
}