Well-Posedness for a System of Generalized KdV-Type Equations Driven by White Noise

  1. Aissa Boukarou
  2. Mohammadi Begum Jeelani
  3. Nouf Abdulrahman Alqahtani
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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 Itô formula and a fixed point argument. Our result improves the local well-posedness result of Gomes and Pastor \cite{gomes2021solitary}.

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  1. Version published to 10.20944/preprints202511.0217.v1