This study demonstrates well-posedness in a coupled KdV system driven by Wiener noise, highlighting fixed-point techniques.
In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg–de Vries system driven by a cylindrical Wiener process. We prove local well-posedness for data in Hs×Hs, with s>12. The key methods that we used in this paper are multilinear estimates in Bourgain spaces, the Itô formula, and a fixed-point argument.
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Boukarou et al. (2025) studied this question.
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