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PreprintCC BY 4.0HAL

Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schrödinger equation with well prepared random initial data.

  • Enguerrand Brun
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Abstract

We prove a long time well-posedness result for a quadratic non-linear Schrödinger equation with random well prepared initial conditions in dimension d ≥ 1. In some regimes, we derive the Wave Kinetic equation associated with the equation in dimension d ≥ 5, almost up to the kinetic time to the power d/(d + 1). Our analysis relies on the ideas introduced by Deng and Hani.

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Cite

BibTeXRIS
BibTeX
@misc{brun2026long,
  title = {{Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schrödinger equation with well prepared random initial data.}},
  author = {Enguerrand Brun},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28093},
  eprint = {2609.28093},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05760949v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schrödinger equation with well prepared random initial data.
AU  - Enguerrand Brun
PY  - 2026
DA  - 2026/09/23
PB  - HAL
DO  - 10.48550/arxiv.2609.28093
UR  - https://hal.science/hal-05760949v2
AB  - We prove a long time well-posedness result for a quadratic non-linear Schrödinger equation with random well prepared initial conditions in dimension d ≥ 1. In some regimes, we derive the Wave Kinetic equation associated with the equation in dimension d ≥ 5, almost up to the kinetic time to the power d/(d + 1). Our analysis relies on the ideas introduced by Deng and Hani.
ER  -