The IVP for the dispersion generalized Benjamin-Ono equation in weighted   Sobolev spaces
  We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model. 
German Fonseca, Felipe Linares and Gustavo Ponce
math.AP