{
  "abstract": "The purpose of this work is to provide a broader framework for analyzing the 1D mass-subcritical inhomogeneous nonlinear Schrödinger equation (INLS) \\[iu_t + u_{xx} \\pm |x|^{-b}|u|^{α-1}u=0, \\quad 1<α< 5-2b\\; \\text{and}\\; 0< b\\leq 1/4.\\] in Sobolev spaces of negative order, reaching almost critical Sobolev spaces by working in Fourier-Lebesgue and modulation spaces. More precisely, we establish low-regularity well-posedness in the Fourier-Lebesgue $\\widehat{L}^{p}$ spaces for $4/3<p<8$. Primarily, we prove global well-posedness for arbitrarily large initial data via the data decomposition method adapted for the Fourier-Lebesgue spaces, with generalized Strichartz estimates for $p<2$ and classical Strichartz estimates for $p>2$. Furthermore, we obtain analogous results for (INLS) in modulation spaces $M^{p,p'}$ for $4/3<p<2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30777",
  "author_total": 3,
  "authors": [
    {
      "name": "Divyang G. Bhimani"
    },
    {
      "name": "Diksha Dhingra"
    },
    {
      "name": "Vijay Kumar Sohani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9w1bff6vz8ha5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30777",
  "fulltext_url": null,
  "id": "9w1bff6vz8ha5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30777",
  "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": "W7204892071",
  "pdf_url": "https://arxiv.org/pdf/2608.30777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9w1bff6vz8ha5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2608.30777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces",
  "title_text": "Inhomogeneous NLS in negative Sobolev spaces via Fourier-Lebesgue and modulation spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/9w1bff6vz8ha5",
  "venue": "arXiv",
  "versions": []
}