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arXiv · 2505.24271

Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS

Tadahiro Oh·Yuzhao Wang
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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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Tadahiro Oh, Yuzhao Wang. 2025-05-30. Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS. https://arxiv.org/abs/2505.24271

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