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Ill-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity $|u|^2$

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  • We are concerned with the ill-posedness issue for the nonlinear Schrödinger equation with the quadratic nonlinearity $|u|^2$ and prove the norm inflation in the dimensions $1 \le n \le 3$. This is the extension of the ill-posed result by Kishimoto-Tsugawa [12] in one dimension and also the remaining case of Iwabuchi-Ogawa [7].
    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35A01.


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