Abstract
The nonlinear D-S equations on R d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H s 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.
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