White noise for KdV and mKdV on the circle
arXiv:1007.1954
Abstract
We survey different approaches to study the invariance of the white noise for the periodic KdV. We mainly discuss the following two methods. First, we discuss the PDE method, following Bourgain \cite{BO4}, in a general framework. Then, we show how it can be applied to the low regularity setting of the white noise for KdV by introducing the Besov-type space \hat{b}^s_{p, \infty}, sp< -1. Secondly, we describe the probabilistic method by Quastel, Valkó, and the author \cite{OQV}. We also use this probabilistic approach to study the white noise for mKdV.
26 pages. To appear in RIMS Kokyuroku Bessatsu
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Cited by in corpus (6)
- Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
- Invariance of white noise for KdV on the line
- Solving the 4NLS with white noise initial data
- Interpolation of Gibbs measures with White Noise for Hamiltonian PDE
- Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation
- Periodic Stochastic Korteweg-de Vries Equation