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

Masahito Ohta

doi:10.3934/cpaa.2018080

Article Contents

2018, Volume 17, Issue 4: 1671-1680. Doi: 10.3934/cpaa.2018080

This issue Previous Article Logarithmic Sobolev and Shannon's inequalities and an application to the uncertainty principle Next Article On the local wellposedness of free boundary problem for the Navier-Stokes equations in an exterior domain

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

Masahito Ohta

Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Received: May 31, 2017

Revised: November 30, 2017

Published: April 2018

The author is supported by JSPS KAKENHI Grant Number 15K04968.

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Abstract

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.

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

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References

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