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

TL;DR

This paper establishes local well-posedness for a stochastic coupled generalized Korteweg-de Vries system driven by white noise, using advanced mathematical techniques to improve previous results.

Contribution

It proves local well-posedness for the stochastic coupled gKdV system in lower regularity spaces, enhancing prior work by Gomes and Pastor.

Findings

Proves local well-posedness for s > 1/2

Uses multilinear estimates in Bourgain spaces

Improves previous results on stochastic gKdV systems

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}.