Analysis of the (CR) equation in higher dimensions
  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. 
T. Buckmaster, P. Germain, Z. Hani, J. Shatah
math.AP