Analysis of (CR) in higher dimension

Tristan Buckmaster, Pierre Germain, Zaher Hani, Jalal Shatah

Research output: Contribution to journalArticle

Abstract

This article is devoted to the analysis of the continuous resonant (CR) equation, in dimensions greater than 2. This equation arises as the large box (or high frequency) limit of the nonlinear Schrödinger equation on the torus, and was derived in a companion paper by the same authors. We initiate the investigation of the structure of (CR), its local well-posedness, and the existence of stationary waves.

Original languageEnglish (US)
Pages (from-to)1265-1280
Number of pages16
JournalInternational Mathematics Research Notices
Volume2019
Issue number4
DOIs
StatePublished - Jan 1 2019

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Higher Dimensions
Local Well-posedness
Torus
Nonlinear Equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Analysis of (CR) in higher dimension. / Buckmaster, Tristan; Germain, Pierre; Hani, Zaher; Shatah, Jalal.

In: International Mathematics Research Notices, Vol. 2019, No. 4, 01.01.2019, p. 1265-1280.

Research output: Contribution to journalArticle

Buckmaster, Tristan ; Germain, Pierre ; Hani, Zaher ; Shatah, Jalal. / Analysis of (CR) in higher dimension. In: International Mathematics Research Notices. 2019 ; Vol. 2019, No. 4. pp. 1265-1280.
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