{
  "abstract": "Motivated by dissipative approximations of the three-dimensional focusing energy-critical nonlinear Schrödinger equation, we study the inviscid and zero-dispersion limits for general energy-critical complex Ginzburg-Landau equations in dimensions $3\\le d\\le6$. We develop a new framework for these limits that does not require a global theory for the limiting equation. For limiting data in $H^1$, we prove strong convergence in the critical space, in particular in $L_t^\\infty H_x^1$, on every compact subinterval of the maximal lifespan of the limiting solution. This includes strong $H^1$ inviscid convergence to the 3D focusing energy-critical NLS without higher regularity of the limiting data. The diffusion and nonlinear coefficients may vary independently, and both focusing and defocusing cases are treated. Both limits use coefficient-uniform critical stability. The inviscid argument uses low-frequency truncation to overcome the derivative loss at $H^1$, whereas uniform parabolic smoothing yields a quantitative $H^1$ estimate in the zero-dispersion limit. Moreover, for the inviscid limit, we prove the required homogeneous Strichartz estimates and obtain the retarded estimates by establishing a uniform retarded double-endpoint bound for the critical forcing space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24088",
  "author_total": 3,
  "authors": [
    {
      "name": "Lingbang Gao"
    },
    {
      "name": "Jie Xin"
    },
    {
      "name": "Yunrui Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fyehc3dw1bbd2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24088",
  "fulltext_url": null,
  "id": "fyehc3dw1bbd2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24088",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7204225804",
  "pdf_url": "https://arxiv.org/pdf/2608.24088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fyehc3dw1bbd2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2608.24088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24088"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Singular limits for general energy-critical complex Ginzburg-Landau equations",
  "title_text": "Singular limits for general energy-critical complex Ginzburg-Landau equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/fyehc3dw1bbd2",
  "venue": "arXiv",
  "versions": []
}