Existence of mild solution to stochastic extended Korteweg - de Vries equation

TL;DR

This paper investigates the existence and uniqueness of local mild solutions for a stochastic Korteweg-de Vries type equation with additive noise, and explores conditions for extending these solutions globally.

Contribution

It provides new sufficient conditions for the existence, uniqueness, and potential globalization of mild solutions to stochastic KdV-type equations.

Findings

Established conditions for local mild solution existence and uniqueness.

Discussed criteria for extending solutions globally.

Contributed to the mathematical understanding of stochastic KdV equations.

Abstract

In the paper we consider stochastic Korteweg - de Vries - type equation. We give sufficient conditions for the existence and uniqueness of local mild solution to the equation with additive noise. We discuss possibility of globalization of mild solution, as well.