The stochastic Korteweg–de Vries equation on a bounded domain

摘要

This paper considers the stochastic Korteweg–de Vries equation on a bounded domain. The existence of a weak martingale solution is discussed by the Galerkin’s approximation and compactness method. Based on this result, we establish the Unique Continuation Property for the stochastic Korteweg–de Vries equation.