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PreprintCC BY 4.0arXiv

Normal form approach to unconditional well-posedness of the periodic stochastic Korteweg-de Vries equation with an additive noise

  • Damiano Greco
  • Tadahiro Oh
  • Philippe Sosoe
  • Yuzhao Wang
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Abstract

We develop a stochastic normal form method for stochastic dispersive equations. As a model example, we study the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the circle. By replacing integration by parts (in time) in the deterministic setting with Ito's product formula in the current stochastic setting, we transform SKdV with an additive noise into a stochastic normal form equation with additive and multiplicative noises. We then use the stochastic normal form equation to prove optimal pathwise unconditional global well-posedness of SKdV in L2(𝕋).

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Cite

BibTeXRIS
BibTeX
@misc{greco2026normal,
  title = {{Normal form approach to unconditional well-posedness of the periodic stochastic Korteweg-de Vries equation with an additive noise}},
  author = {Damiano Greco and Tadahiro Oh and Philippe Sosoe and Yuzhao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29935},
  eprint = {2610.29935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29935},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Normal form approach to unconditional well-posedness of the periodic stochastic Korteweg-de Vries equation with an additive noise
AU  - Damiano Greco
AU  - Tadahiro Oh
AU  - Philippe Sosoe
AU  - Yuzhao Wang
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29935
UR  - https://arxiv.org/abs/2610.29935
AB  - We develop a stochastic normal form method for stochastic dispersive equations. As a model example, we study the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the circle. By replacing integration by parts (in time) in the deterministic setting with Ito's product formula in the current stochastic setting, we transform SKdV with an additive noise into a stochastic normal form equation with additive and multiplicative noises. We then use the stochastic normal form equation to prove optimal pathwise unconditional global well-posedness of SKdV in L^2(𝕋).
ER  -