The stochastic Korteweg-de Vries equation in L2 (ℝ)

Abstract

We present here two results of global existence and uniqueness of the Cauchy problem concerning the Korteweg-de Vries equation forced by a random term of white noise type in the functional framework of weighted spaces onL2(R). This work is motivated by both physical experiments where a forced generation of weakly nonlinear waves by localized disturbances was observed [1,15] and a result of uniqueness in weighted space in the homogeneous case [8,14]. © 1999 Academic Press.