Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Spitz, Martin, Zhang, Deng, Zhao, Zhenqi
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909604987797504
author Spitz, Martin
Zhang, Deng
Zhao, Zhenqi
author_facet Spitz, Martin
Zhang, Deng
Zhao, Zhenqi
contents In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schrödinger 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_05421
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations
Spitz, Martin
Zhang, Deng
Zhao, Zhenqi
Analysis of PDEs
Probability
In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schrödinger 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.
title Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations
topic Analysis of PDEs
Probability
url https://arxiv.org/abs/2505.05421