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arXiv · 2505.22478

Invariant Gibbs measures for the one-dimensional quintic nonlinear Schr\"odinger equation in infinite volume

Bjoern Bringmann·Gigliola Staffilani
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Abstract

We prove the invariance of the Gibbs measure for the defocusing quintic nonlinear Schr\"odinger equation on the real line. This builds on earlier work by Bourgain, who treated the cubic nonlinearity. The key new ingredient is a growth estimate for the infinite-volume $\Phi^{p+1}_1$-measures, which is proven via the stochastic quantization method.

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Bjoern Bringmann, Gigliola Staffilani. 2025-05-28. Invariant Gibbs measures for the one-dimensional quintic nonlinear Schr\"odinger equation in infinite volume. https://arxiv.org/abs/2505.22478

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