Analysis of the (CR) equation in higher dimensions

T. Buckmaster; P. Germain; Z. Hani; J. Shatah

Analysis of the (CR) equation in higher dimensions

Analysis of PDEs 2016-10-19 v1

Authors: T. Buckmaster , P. Germain , Z. Hani , J. Shatah

Abstract

This paper 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 Schrodinger 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.

Keywords

continuous resonant equation nonlinear Schrödinger equation local well-posedness stationary waves high frequency limit

Cite

@article{arxiv.1610.05736,
  title  = {Analysis of the (CR) equation in higher dimensions},
  author = {T. Buckmaster and P. Germain and Z. Hani and J. Shatah},
  journal= {arXiv preprint arXiv:1610.05736},
  year   = {2016}
}

Comments

13 pages. This is a companion paper to arXiv:1610.03824 [math.AP]

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