Remarks on the orbital instability of standing waves for thewave-Schrödinger system in higher dimensions

Hiroaki Kikuchi

doi:10.3934/cpaa.2010.9.351

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2010, Volume 9, Issue 2: 351-364. Doi: 10.3934/cpaa.2010.9.351

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Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions

Hiroaki Kikuchi^1,

1.
Department of Mathematics, Hokkaido University Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810

Received: September 30, 2008

Revised: July 31, 2009

Published: February 2010

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Abstract

In this paper, we study the orbital instability of standing wave for the wave-Schrödinger system in 4 or 5 space dimensions. More precisely, we show that there exists a solution which is not uniformly bounded no matter how the initial data is close to the standing wave.

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Mathematics Subject Classification: Primary: 35Q55, 35B35; Secondary: 35J20.

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