Well-posedness of the stochastic KdV–Burgers equation

Geordie Richards

Stochastic Processes and their Applications, 2014, vol. 124, issue 4, 1627-1647

Abstract: 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.

Keywords: Well-posedness; Stochastic PDEs; White noise invariance (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:4:p:1627-1647

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DOI: 10.1016/j.spa.2013.12.008

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