  The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been
proposed as a model for a randomly growing interface. This equation can be
reformulated as a stochastic Burgers equation. We study a stochastic
KdV-Burgers equation as a toy model for this stochastic Burgers equation. Both
of these equations formally preserve spatial white noise. We are interested in
rigorously proving the invariance of white noise for the stochastic KdV-Burgers
equation. This paper establishes a result in this direction. After smoothing
the additive noise (by less than one spatial derivative), we establish (almost
sure) local well-posedness of the stochastic KdV-Burgers equation with white
noise as initial data. We also prove a global well-posedness result under an
additional smoothing of the noise.
