{
  "abstract": "In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with a nonlinearity combining a logarithmic term and a local nonlinearity which has polynomial growth. Our main result is the construction of solutions in the energy space $W_1(R^d)$ in the subcritical case. We also discuss a sufficient condition for global existence in the $L^2$-critical case in each of these spaces. Moreover, we establish a more general Cauchy theory in the space $\\Sigma_\\alpha$, as introduced without details in [6].",
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  "article_type": null,
  "arxiv": "2609.19217",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Bensaid"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c90brtkk7k491.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19217",
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  "id": "c90brtkk7k491",
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  "landing_url": "https://hal.science/hal-05749120v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05749120/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c90brtkk7k491.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05749120",
      "source": "hal",
      "url": "https://hal.science/hal-05749120v1"
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      "native_id": "2609.19217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19217"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Cauchy problem for logarithmic Schrödinger equation with a perturbation of power law nonlinearity",
  "title_text": "The Cauchy problem for logarithmic Schrödinger equation with a perturbation of power law nonlinearity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/c90brtkk7k491",
  "venue": "HAL",
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}