Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS
Analysis of PDEs
2025-06-02 v1 Probability
Abstract
In a seminal paper (1996), Bourgain proved invariance of the Gibbs measure for the defocusing cubic nonlinear Schr\"odinger equation on the two-dimensional torus by constructing local-in-time solutions in a probabilistic manner. In this note, we revisit and streamline his argument, using the random tensor estimate developed by Deng, Nahmod, and Yue (2022).
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Cite
@article{arxiv.2505.24271,
title = {Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS},
author = {Tadahiro Oh and Yuzhao Wang},
journal= {arXiv preprint arXiv:2505.24271},
year = {2025}
}
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40 pages