Well-posedness results for the dispersion generalized Benjamin-Ono   equation via the contraction principle
  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 via contraction principle under minimal requirements in the weighted order of the space. One of our new main ideas is the deduction of a pointwise estimate concerning the group describing the solution of the linear problem and the fractional weights. 
Germ\'an Fonseca, Felipe Linares, Gustavo Ponce
math.AP