Ill-Posedness for the Nonlinear Davey-Stewartson Equation

The nonlinear D-S equations on Rd, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space Hs whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.