Invariance of the White Noise for KdV
By Tadahiro Oh. 2009
56 citations recorded by the source corpus.
We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space $${\widehat{b}^s_{p,\infty}}$$ , sp < −1, contains the support of the white noise. Then, we prove local well-posedness in $${\widehat{b}^s_{p, \infty}}$$ for p = 2 + , $${s = -\frac{1}{2}+}$$ such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21].
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/85c9776139bb61aac9a1d90db027cea0413401c7
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In Applied Mathematics
- Tadahiro Oh
- Gigliola Staffilani
- Andrea R. Nahmod
- Nikolay Tzvetkov
- Nicola Visciglia
- Luc Rey-Bellet
- James E. Colliander
- D. Tataru
In Mathematical Physics
- Tadahiro Oh
- Gigliola Staffilani
- Andrea R. Nahmod
- Nikolay Tzvetkov
- James E. Colliander
- Nicola Visciglia
- Luc Rey-Bellet
- Terence Tao
Citations in the corpus
- INVARIANT WEIGHTED WIENER MEASURES AND ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE PERIODIC DERIVATIVE NLS. (2010, methodology): “Oh [33, 34, 35, 36] for the periodic KdV-type coupled systems, Schrödinger-Benjamin-Ono system and white noise for the KdV equation.”
- Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation (2014, background): “On the other hand, in the case of the KdV equation, it is known that the white noise is invariant under a well-defined dynamics, see [17,19,20].”
- Almost sure well-posedness of the cubic nonlinear Schr\ (2009, background): “) Invariance of white noise has recently been established for the KdV equation on T [30, 26, 28].”