Almost sure global nonlinear smoothing for the 2D NLS
Abstract
In this article, we prove an almost-sure global in time nonlinear smoothing effect for NLS on the two-dimensional torus. For deterministic data, this phenomenon was proved for the NLS on the circle by Erdogan--Tzirakis, which remains unknown on multidimensional torus. Our argument is based on a quantitative quasi-invariance of Gaussian measures with covariance operator (1-)-s for s>2.
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