The Stochastic Korteweg–de Vries Equation inL2( )

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( ). 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].