Ill-Posedness of the Cubic Nonlinear Half-Wave Equation and Other Fractional NLS on the Real Line
Ill-Posedness of the Cubic Nonlinear Half-Wave Equation and Other Fractional NLS on the Real Line
In this paper, we study ill-posedness of cubic fractional nonlinear Schrödinger (NLS) equations. First, we consider the cubic nonlinear half-wave equation on |$\mathbb{R}$|. In particular, we prove the following ill-posedness results: (1) failure of local uniform continuity of the solution map in |$H^s(\mathbb{R})$| for |$s\in (0,\frac 12)$|, and also for …