# Finite-time blowup for a Schr\"odinger equation with nonlinear source term.

@inproceedings{Cazenave2018FinitetimeBF,
title={Finite-time blowup for a Schr\"odinger equation with nonlinear source term.},
author={Thierry Cazenave and Yvan Martel and Lifeng Zhao},
year={2018}
}
We consider the nonlinear Schr\"odinger equation $u_t = i \Delta u + | u |^\alpha u \quad \mbox{on {\mathbb R}^N , \alpha>0,}$ for $H^1$-subcritical or critical nonlinearities: $(N-2) \alpha \le 4$. Under the additional technical assumptions $\alpha\geq 2$ (and thus $N\leq 4$), we construct $H^1$ solutions that blow up in finite time with explicit blow-up profiles and blow-up rates. In particular, blowup can occur at any given finite set of points of ${\mathbb R}^N$. The construction… CONTINUE READING

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## A P ] 3 0 M ay 2 01 9 BLOWUP SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH COMPLEX COEFFICIENT

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## Blowup solutions for the nonlinear Schr\"odinger equation with complex coefficient.

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