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

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

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

1.	Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received June 2008 Revised November 2008 Published February 2009

Abstract
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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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