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# Strong instability of standing waves for nonlinear Schrödinger equations with a partial confinement

The author is supported by JSPS KAKENHI Grant Number 15K04968.
• We study the instability of standing wave solutions for nonlinear Schrödinger equations with a one-dimensional harmonic potential in dimension $N≥2$ . We prove that if the nonlinearity is $L^2$ -critical or supercritical in dimension $N-1$ , then any ground states are strongly unstable by blowup.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B35.

 Citation:

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