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

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March 2010, 9(2): 351-364. doi: 10.3934/cpaa.2010.9.351

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

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

Received October 2008 Revised August 2009 Published December 2009

Abstract
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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.

Keywords: variational methods., standing waves, Wave-Schrödinger system, orbital instability.

Mathematics Subject Classification: Primary: 35Q55, 35B35; Secondary: 35J2.

Citation: Hiroaki Kikuchi. Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions. Communications on Pure & Applied Analysis, 2010, 9 (2) : 351-364. doi: 10.3934/cpaa.2010.9.351

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