Analysis of (CR) in Higher Dimension. (17th July 2017)

• Record Type: Journal Article
• Authors: Buckmaster, Tristan; Germain, Pierre; Hani, Zaher; Shatah, Jalal
• Is Part Of: International mathematics research notices. Volume 2019:Number 4(2019)
• Page Start: 1265
• Page End: 1280
• Publication Date: 2017-07-17
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx156
• Languages: English
• ISSNs: 1073-7928

Abstract

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.