Martingale solution to stochastic extended Korteweg - de Vries equation

TL;DR

This paper establishes the existence of a martingale solution for a stochastic extended Korteweg-de Vries equation with multiplicative noise, using approximation techniques and compactness methods.

Contribution

It provides the first proof of martingale solutions for this stochastic extended KdV equation, advancing understanding of stochastic nonlinear dispersive PDEs.

Findings

Existence of martingale solutions proven

Method based on two approximations and compactness

Framework applicable to similar stochastic PDEs

Abstract

We study a stochastic extended Korteweg - de Vries equation driven by a multiplicative noise. We prove the existence of a martingale solution to the equation studied. The proof of the solution is based on two approximations of the problem considered and the compactness method.