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PreprintCC BY 4.0HAL

The Cauchy problem for logarithmic Schrödinger equation with a perturbation of power law nonlinearity

  • Mohamed Bensaid
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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 W1(Rd) in the subcritical case. We also discuss a sufficient condition for global existence in the L2-critical case in each of these spaces. Moreover, we establish a more general Cauchy theory in the space Σα, as introduced without details in [6].

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Cite

BibTeXRIS
BibTeX
@misc{bensaid2026cauchy,
  title = {{The Cauchy problem for logarithmic Schrödinger equation with a perturbation of power law nonlinearity}},
  author = {Mohamed Bensaid},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19217},
  eprint = {2609.19217},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05749120v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Cauchy problem for logarithmic Schrödinger equation with a perturbation of power law nonlinearity
AU  - Mohamed Bensaid
PY  - 2026
DA  - 2026/09/14
PB  - HAL
DO  - 10.48550/arxiv.2609.19217
UR  - https://hal.science/hal-05749120v1
AB  - 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 Σ_α, as introduced without details in [6].
ER  -