Nonlinear Schrödinger equation for the twisted Laplacian in the critical case

We prove well-posedness of solution to the nonlinear Schrödinger equation associated to the twisted Laplacian on $\C^n$ for a general class of nonlinearities including power type with subcritical case $0\leq α<\frac{2}{n-1}$, see Ratnakumar, Sohani (J. Funct. Anal. 2013). In this paper, we consider critical case $α=\frac{2}{n-1}$ with $n\geq 2$. Our approach is based on truncation of the given nonlinearity $G$, which is used by Cazenave Weissler (1989). We obtain solution for the truncated problem. We obtain solution to the original problem by passing to the limit.

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