Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian

We prove global existence of the Cauchy problem of a Schrodinger equation with the logarithmic laplacian and a pure power linearity. We address the focusing and the defocusing cases, and we obtained a sharp blow-up in time result.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39146
Primary Topic
Advanced Mathematical Physics Problems
Type
preprint
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preprint

Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian

Hichem Hajaiej
arXiv (Cornell University)
Advanced Mathematical Physics Problems
preprint

Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian

Hichem Hajaiej
preprint en

Abstract

We prove global existence of the Cauchy problem of a Schrodinger equation with the logarithmic laplacian and a pure power linearity. We address the focusing and the defocusing cases, and we obtained a sharp blow-up in time result.

arXiv (Cornell University)
Advanced Mathematical Physics Problems
DOIOpen Access PDFOpenAlex
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Power-Type Nonlinear Schrödinger Equations with the Logarithmic Laplacian — Hichem Hajaiej · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS