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

Sijia Zhong; Daoyuan Fang

doi:10.3934/cpaa.2009.8.1117

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2009, Volume 8, Issue 3: 1117-1132. Doi: 10.3934/cpaa.2009.8.1117

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

Sijia Zhong^1, and
Daoyuan Fang^1,

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027

Received: June 2008

Revised: November 2008

Published: May 2009

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Abstract

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].

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B05.

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