Well-posednesss of strongly dispersive two-dimensional surface waves   Boussinesq systems
  We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the {\it strongly dispersive} ones with focus on the "KdV-KdV" system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical KdV equation. 
Felipe Linares, Didier Pilod, Jean-Claude Saut
math.AP