Analysis of (CR) in Higher Dimension. (17th July 2017) - Buckmaster, Tristan; Germain, Pierre; Hani, Zaher; Shatah, Jalal
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.