Well-posedness of the stochastic KdV-Burgers equation

We are interested in rigorously proving the invariance of white noise under the flow of a stochastic KdV Burgers equation. This paper establishes a result in this direction. After smoothing the additive noise (by a fractional spatial derivative), we establish (almost sure) local well-posedness of the stochastic KdV Burgers equation with white noise as initial data. Next we observe that spatial white noise is invariant under the projection of this system to the first N > 0 modes of the trigonometric basis. Finally, we prove a global well-posedness result under an additional smoothing of the noise. (C) 2013 Elsevier B.V. All rights reserved.