Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS

Arpad Benyi, Tadahiro Oh, Oana Pocovnicu

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

We consider a randomization of a function on ℝ^d that is naturally associated to the Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized functions enjoy better integrability, thus allowing us to improve the Strichartz estimates for the Schrödinger equation. As an example, we also show that the energy-critical cubic nonlinear Schrödinger equation on ℝ^4 is almost surely locally well-posed with respect to randomized initial data below the energy space.
Original languageEnglish
Title of host publicationExcursions in Harmonic Analysis
Subtitle of host publicationThe February Fourier Talks at the Norbert Wiener Center
EditorsR. Balan, M. Begue, J.J. Benedetto, W. Czaja, K.A. Okoudjou
PublisherBasel: Birkhauser Verlag
Pages3-25
Number of pages20
Volume4
ISBN (Electronic)978-3-319-20188-7
ISBN (Print)978-3-319-20187-0
DOIs
Publication statusPublished - Oct 2015

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009

Keywords

  • nonlinear Schrödinger equation
  • almost sure well-posedness
  • modulation space
  • Wiener decomposition
  • Strichartz estimate
  • Fourier restriciton norm method

Fingerprint

Dive into the research topics of 'Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS'. Together they form a unique fingerprint.

Cite this