Stochastic nonlinear Schrödinger equation with almost space-time white noise

Research output: Contribution to journalArticlepeer-review

Authors

Colleges, School and Institutes

External organisations

  • Heriot-Watt University, Edinburgh
  • University of Edinburgh

Abstract

We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space-time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation).

Details

Original languageEnglish
Pages (from-to)44-67
Number of pages24
JournalJournal of the Australian Mathematical Society
Volume109
Issue number1
Publication statusPublished - 1 Aug 2020

Keywords

  • Fourier Lebesgue spaces, Stochastic nonlinear Schrodinger equation, Well-posedness, White noise

ASJC Scopus subject areas