Almost sure pointwise convergence for the 2D periodic quintic NLS
Daniel Eceizabarrena, Pablo Merino
Abstract
We prove probabilistic pointwise convergence to the initial datum for the 2D periodic quintic NLS for data in Hs( T2) with s > 0. This is an improvement with respect to the deterministic setting, in which convergence is known to fail if s < 1/3. The proof is based on a nonlinear maximal characterization for convergence, Bourgain's linear-nonlinear decomposition and the corresponding nonlinear smoothing for which we employ random tensor estimates.
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