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.