{
  "abstract": "We study nonlinear Schrödinger equations with nonlinear Stratonovich noise \\begin{equation*} \\mathrm{d} u\\,=\\, i\\bigl[ Δu \\,+\\, λ|u|^{p-1}u\\bigr] \\, \\mathrm{d} t \\,+\\,i|u|^{(q-1)/2}u\\circ \\mathrm{d} {W}, \\end{equation*} in their energy space $H^1(\\mathbb R^d;\\mathbb C)$. By combining the stochastic Strichartz estimates derived in [Potential Anal. 41 (2014), pp.\\ 269--315] with the approach from [Ann.\\ Inst.\\ H.\\ Poincaré Phys.\\ Théor.\\ 46 (1987), pp.\\ 113--129] we obtain local well-posedness for all energy-subcritical nonlinearities $p,q\\in [1, 1+4/(d-2)_+)$ together with a corresponding blow-up alternative. For a linear multiplicative noise $q=1$, a real-valued noise $W$ and a defocusing nonlinearity $λ\\le 0$, we check this blow-up condition using a bound on the energy, resulting in the global well-posedness of the equation. If both nonlinearities are mass-subcritical, i.e., $p,q\\in [1, 1+4/d)$, we provide an improved blow-up criterion involving the $L^2(\\mathbb R^d;\\mathbb C)$-norm. Using the conservation of mass for real-valued $W$, we obtain global well-posedness also in this case. Compared to previous results on stochastic nonlinear Schrödinger equations, we thereby improve the range of exponents $p$ and $q$ and the spatial regularity assumption on the noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10417",
  "author_total": 2,
  "authors": [
    {
      "name": "Max Sauerbrey"
    },
    {
      "name": "Joris van Winden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64c2pstctfsjm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10417",
  "fulltext_url": null,
  "id": "64c2pstctfsjm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10417",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212174858",
  "pdf_url": "https://arxiv.org/pdf/2609.10417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64c2pstctfsjm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Schrödinger equation with fluctuating nonlinearity in the energy space",
  "title_text": "The Schrödinger equation with fluctuating nonlinearity in the energy space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/64c2pstctfsjm",
  "venue": "arXiv",
  "versions": []
}