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We improve the results about the well-posedness of the regularized fractional dispersive equation (1 +  D x  α  ) u t   +  u x   +  uu x   = 0 when 0 &lt;  α  ≤ 1. When  #x03B1;  &lt; 1, the existence and uniqueness of vanishing viscosity solution is proved.

Remark on the well-posedness of weakly dispersive equations