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On blow up NLS with a multiplicative noise

Analysis of PDEs 2026-04-07 v2 Probability

Abstract

It is of significant interest to understand whether a noise will speed up or prevent blow up. Under certain nondegenerate conditions, \cite{dD2005Blowup} proved a multiplicative noise will speed up blow up of NLS, in the sense that, blow up can happen in any short time with positive probability. We prove that such probability is indeed quite small, and provide a large deviation type upper bound.

Keywords

Cite

@article{arxiv.2601.19330,
  title  = {On blow up NLS with a multiplicative noise},
  author = {Chenjie Fan and Junzhe Wang},
  journal= {arXiv preprint arXiv:2601.19330},
  year   = {2026}
}

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13 pages, all comments are welcome