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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

Hiroaki Kikuchi 1,

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

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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