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May  2009, 8(3): 1117-1132. doi: 10.3934/cpaa.2009.8.1117

$L^2$-concentration phenomenon for Zakharov system below energy norm II

Sijia Zhong 1, and  Daoyuan Fang 1,

1. 

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received  June 2008 Revised  November 2008 Published  February 2009

In this paper, we will prove a $L^2$-concentration result of Zakharov system in space dimension two, with initial data $(u_0,n_0,n_1)\in H^s\times L^2\times H^{-1}$ ($\frac {1 2}{1 3} < s < 1$), when blow up of the solution happens, by resonant decomposition and I-method, which is an improvement of [13].
Keywords: blow up, $L^2$-concentration, global existence., Zakharov system in space dimension two.
Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B0.
Citation: Sijia Zhong, Daoyuan Fang. $L^2$-concentration phenomenon for Zakharov system below energy norm II. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1117-1132. doi: 10.3934/cpaa.2009.8.1117
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