We study 1D NLS with non-gauge-invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. Moreover, the existence of blowup solutions has been studied by focusing on the behavior of the Fourier 0 mode of solutions. In this paper, the precise blow up criteria for the Cauchy problem is shown in a hat Lebesgue space by studying the interaction between the Fourier 0 mode and oscillation of solutions. Namely, solutions in the hat Lebesgue space are shown to blow up if they are different from the trivial ones.
MSC Codes 35Q55
|Publication status||Published - 2020 Sep 9|
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