Regularization by noise for the energy- and mass-critical nonlinear Schr\"odinger equations

Martin Spitz; Deng Zhang; Zhenqi Zhao

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arXiv · 2505.05421

Regularization by noise for the energy- and mass-critical nonlinear Schr\"odinger equations

Martin Spitz·Deng Zhang·Zhenqi Zhao

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Abstract

In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schr\"odinger equations. We show that for any deterministic data, the probability that the corresponding solution exists globally and scatters goes to one as the strength of the non-conservative noise goes to infinity. The proof relies on the rescaling transform and a new observation on the rapid uniform decay of geometric Brownian motions after short time.

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Martin Spitz, Deng Zhang, Zhenqi Zhao. 2025-05-08. Regularization by noise for the energy- and mass-critical nonlinear Schr\"odinger equations. https://arxiv.org/abs/2505.05421

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