Title: Strong instability of standing waves for nonlinear Schrödinger equations with a partial confinement,
Abstract: We study the instability of standing wave solutions for nonlinear
Schrödinger equations with a one-dimensional harmonic potential in
dimension $N\ge 2$. 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.