Analysis of (CR) in higher dimension

Tristan Buckmaster; Pierre Germain; Zaher Hani; Jalal Shatah

doi:10.1093/imrn/rnx156

Analysis of (CR) in higher dimension

Tristan Buckmaster, Pierre Germain, Zaher Hani, Jalal Shatah

Mathematics

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1 Scopus citations

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 language	English (US)
Pages (from-to)	1265-1280
Number of pages	16
Journal	International Mathematics Research Notices
Volume	2019
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnx156
State	Published - Feb 20 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnx156

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AU - Hani, Zaher

AU - Shatah, Jalal

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Y1 - 2019/2/20

N2 - 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.

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Analysis of (CR) in higher dimension

Abstract

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