{
  "abstract": "We study a generalized Gross-Pitaevskii equation arising in the mean-field description of exciton-polariton Bose-Einstein condensates. The dynamics close to macroscopic wave functions $r_0e^{iω_0 t +ik_0x}$ is governed by a stabilizing relaxation mechanism without suppressing dispersive blow-up. We show that this competition yields $L^\\infty$-regularity thresholds. More precisely, we construct solutions for which arbitrarily small perturbations from $C^4_b$ can develop finite time blow-up in $C^3_b$ whereas perturbations from $C^{4+η}_b$ for every $η>0$, satisfy a global-in-time $C^3_b$-stability estimate. The stability analysis is carried out in modulation spaces $M_{\\infty,1}^k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20888",
  "author_total": 1,
  "authors": [
    {
      "name": "Joannis Alexopoulos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enagn44ycapr0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20888",
  "fulltext_url": null,
  "id": "enagn44ycapr0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20888",
  "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": "W7222537781",
  "pdf_url": "https://arxiv.org/pdf/2610.20888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enagn44ycapr0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^\\infty$-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability",
  "title_text": "L^∞-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/enagn44ycapr0",
  "venue": "arXiv",
  "versions": []
}