A Coupled Generalized Korteweg-de Vries System Driven by White Noise

Aissa Boukarou

A Coupled Generalized Korteweg-de Vries System Driven by White Noise

Analysis of PDEs 2025-10-31 v2

Authors: Aissa Boukarou

Abstract

In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg-de Vries system driven by white noise. We prove local well-posedness for data in $H^{s} \times H^{s},$ with $s>1/2$ . The key ingredients that we used in this paper are multilinear estimates in Bourgain spaces, the It\^o formula and a fixed point argument. Our result improves the local well-posedness result of Gomes and Pastor \cite{gomes2021solitary}.

Keywords

well-posedness

Cite

@article{arxiv.2510.23843,
  title  = {A Coupled Generalized Korteweg-de Vries System Driven by White Noise},
  author = {Aissa Boukarou},
  journal= {arXiv preprint arXiv:2510.23843},
  year   = {2025}
}

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