On invariant Gibbs measures for the generalized KdV equations

2015/09/23 by Oh, Tadahiro, Richards, Geordie, Thomann, Laurent · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1509.06873

Abstract

We consider the defocusing generalized KdV equations on the circle. In particular, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure. In handling a nonlinearity of an arbitrary high degree, we make use of the Hermite polynomials and the white noise functional.

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• Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation

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