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

December 11, 2025Open Access

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

Key Points

The study aims to investigate the Cauchy problem for a coupled generalized KdV system influenced by noise.
Proved local well-posedness for data in Hs×Hs with s>12.
Employed multilinear estimates in Bourgain spaces.
Utilized the Itô formula and fixed-point argument.
Local well-posedness established in the context of the analyzed KdV system.

Abstract

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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Cite This Study

Boukarou et al. (Thu,) studied this question.

synapsesocial.com/papers/69401b172d562116f28f72c8 https://doi.org/https://doi.org/10.3390/axioms14120911

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